21秋福师《实变函数》考前练兵
《实变函数》考前练兵1.[单选题] 下列正确的是( )
A.<img id="PIwipmtitem20210721105816417.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIwipmtitem20210721105816417.png?Expires=1942196296&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=kOf20uxFjKCa9DG016f%2Bbqf500M%3D" />
B.<img id="PIgklfxitem20210721105816546.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIgklfxitem20210721105816546.png?Expires=1942196296&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=uqNiRFvzIt6%2B%2F%2Flsej%2BUKhQqp2Y%3D" />
C.<img id="PIjganjitem20210721105816863.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIjganjitem20210721105816863.png?Expires=1942196296&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=SunGFSA4LaKf20aidbOJ6QdDC9M%3D" />
D.<img id="PIsjmtiitem20210721105816576.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIsjmtiitem20210721105816576.png?Expires=1942196297&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=6IoJ03ETodLTfSK3RYQ9Vd2%2FoJA%3D" />
答:——B——
2.[单选题] 设E为<img id="PImielritem20210721105817162.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PImielritem20210721105817162.png?Expires=1942196297&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=gNgj6tEJXLJoVjtcEAWpXKlJZvY%3D" />中的一个不可测集,令<img id="PIxxzneitem20210721105816886.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIxxzneitem20210721105816886.png?Expires=1942196297&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=aYr40TV%2BAFQPSECv2p44dglYDUw%3D" />,则<img id="PIsojfzitem20210721105817496.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIsojfzitem20210721105817496.png?Expires=1942196295&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=KNf6UM29ItBQrfkXkeqKgEHumUE%3D" />必是( )
A.L可积函数
B.不是L可测函数
C.无界函数
D.连续函数
答:——B——
3.[单选题] 若<img id="PIwexioitem20210721105817690.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIwexioitem20210721105817690.png?Expires=1942196297&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=lnEqByO8nqOXFIr7CzTX%2FNlhzAU%3D" />不是L可测,<img id="PIoidqwitem20210721105817855.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIoidqwitem20210721105817855.png?Expires=1942196297&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=F5pMoQoo3uBqR38sqpDBC9knm4M%3D" />是L可测,则下列正确的是( )
A.<img id="PIbekvxitem20210721105818012.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIbekvxitem20210721105818012.png?Expires=1942196297&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=jdiFx%2FtV8CYKQfrf9Xcd9xTQvNQ%3D" />不是L可测
B.<img id="PIwnlghitem20210721105818195.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIwnlghitem20210721105818195.png?Expires=1942196298&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=fT3lQyMofU0P8XJkracQ01msec0%3D" />不是L可测
C.<img id="PIgsvbtitem20210721105818424.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIgsvbtitem20210721105818424.png?Expires=1942196298&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=0Dtkc23ZyE5mZIlzU%2BT81k28F2U%3D" />是L可测
D.<img id="PItkigditem20210721105818576.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PItkigditem20210721105818576.png?Expires=1942196298&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=8SUyeCBlb3MdXoseJYCJwtUk1bc%3D" />不是L可测
答:——C——
4.[单选题] 若<img id="PIbfsdmitem20210721105818730.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIbfsdmitem20210721105818730.png?Expires=1942196296&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=rgM4UkK0ppz41Wi%2Fx4cq3PL36V8%3D" />和<img id="PIppgtfitem20210721105816985.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIppgtfitem20210721105816985.png?Expires=1942196298&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=r5LFouHHXDhyaxfxGkm9yPm8gH8%3D" />都是<img id="PIjridvitem20210721105818652.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIjridvitem20210721105818652.png?Expires=1942196299&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=pVVBRTQiFMngdqsASUB6Viprm5g%3D" />中开集,且<img id="PIoiqgnitem20210721105818808.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIoiqgnitem20210721105818808.png?Expires=1942196299&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=xyVlbJD91QmgSibnxkz1Vhqr%2BIo%3D" />是<img id="PIbzarwitem20210721105819382.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIbzarwitem20210721105819382.png?Expires=1942196298&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=dV9GQrXMf1rhbNjL%2F%2B7lxItqlls%3D" />的真子集,则( )
A.<img id="PIfczxoitem20210721105817649.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIfczxoitem20210721105817649.png?Expires=1942196299&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=Tf8yM9LRmB5GAD1xDyKFtO%2F2M04%3D" />
B.<img id="PIhlfbtitem20210721105817818.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIhlfbtitem20210721105817818.png?Expires=1942196299&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=3g6%2FAxUlGW6vJpimCqpPt4oOX1A%3D" />
C.<img id="PIehubgitem20210721105819907.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIehubgitem20210721105819907.png?Expires=1942196299&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=%2BXzRc0yofKaxQ2cDiA7kq2OO7%2Bg%3D" />
D.<img id="PIllvpbitem20210721105818110.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIllvpbitem20210721105818110.png?Expires=1942196300&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=g2g3O4Ov2zdC8K%2BhBhuPmSzTLb4%3D" />
答:————
5.[单选题] 若<img id="PIrtbgditem20210721105820207.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIrtbgditem20210721105820207.png?Expires=1942196299&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=9jx%2B%2FfeUogNYa%2BSRemk%2BfyadY2Y%3D" />为L可积函数,则( )
A.<img id="PIelhnsitem20210721105820377.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIelhnsitem20210721105820377.png?Expires=1942196300&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=XU00YpuUH%2BfizUiblpV3bZMTUwU%3D" />连续
B.<img id="PIlshzditem20210721105820508.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIlshzditem20210721105820508.png?Expires=1942196300&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=ZGemyxKv6MKVTKbaqXNMfU7i5HY%3D" />也L可积
C.<img id="PIgrjhbitem20210721105820673.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIgrjhbitem20210721105820673.png?Expires=1942196301&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=qXDxo5deiCPg945EA8j5BisLGwU%3D" />也L可积
D.<img id="PIftnswitem20210721105820415.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIftnswitem20210721105820415.png?Expires=1942196300&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=tqbePJNX9nUOUWrSMMWmsp3%2FC64%3D" />有界
答:————
6.[单选题] 若<img id="PIcqdpvitem20210721105821052.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIcqdpvitem20210721105821052.png?Expires=1942196300&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=rCvfKxofHvEqsLXmOT24EX4k0r8%3D" />且<img id="PIuyojfitem20210721105820913.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIuyojfitem20210721105820913.png?Expires=1942196301&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=%2Bo0ddEuIJqLMP0bXp5OdWsJFWWs%3D" />是L可积,则( )
A.<img id="PIxnmbeitem20210721105821055.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIxnmbeitem20210721105821055.png?Expires=1942196301&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=navYbQ9hnJv675R5QReUOpSsnAQ%3D" />是L可测
B.<img id="PIcjefjitem20210721105821864.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIcjefjitem20210721105821864.png?Expires=1942196301&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=cVjcudZqYNZnEBTND91JMrRSYkY%3D" />是L可积
C.<img id="PInkyakitem20210721105822194.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PInkyakitem20210721105822194.png?Expires=1942196302&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=1YeaLayCHCM38RRR9gcEAjsPoxc%3D" />有界
D.当<img id="PIeosecitem20210721105822376.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIeosecitem20210721105822376.png?Expires=1942196302&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=PHG01kh7RR6u4djrE2vQxQEXwbA%3D" />是L可测时,<img id="PIqjhwiitem20210721105822543.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIqjhwiitem20210721105822543.png?Expires=1942196302&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=xTWDCCCqiZArrb2eZKabt1%2B5yVs%3D" />必L可积
答:————
7.[单选题] 令<img id="PIhvevbitem20210721105822260.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIhvevbitem20210721105822260.png?Expires=1942196302&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=CZjpVZvXhHm825Q%2B1YsXo4WNic0%3D" />,则<img id="PIgymnfitem20210721105822878.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIgymnfitem20210721105822878.png?Expires=1942196302&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=vZ%2Fxd0S9u0MfJztL4uQNRiV787I%3D" />在<img id="PIbyjoxitem20210721105823065.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIbyjoxitem20210721105823065.png?Expires=1942196303&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=b9tffG6p5GCAzOGV1sgdLOSqg1c%3D" />上( )
A.不是L可测
B.不是广义R可积
C.L可积
D.不是L可积
答:————
8.[单选题] 令<img id="PIohrgjitem20210721105821344.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIohrgjitem20210721105821344.png?Expires=1942196303&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=6nzzBD33NjU0hsCkkFPg1hdbU40%3D" />,则<img id="PIrupspitem20210721105823408.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIrupspitem20210721105823408.png?Expires=1942196302&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=%2F3qfvykQmslrVgydA5vljJIjUTI%3D" />在<img id="PIenvpbitem20210721105822958.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIenvpbitem20210721105822958.png?Expires=1942196303&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=LOG3XmpZMBhnuYxVYHRAEMf1Sts%3D" />上( )
A.没有L积分值
B.广义R可积
C.L可积
D.L积分具有绝对连续性
答:————
9.[单选题] 设<img id="PInoclsitem20210721105823361.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PInoclsitem20210721105823361.png?Expires=1942196303&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=MnvMoPgw%2Bn6i2JV3OHtwMVmvZi4%3D" />为<img id="PIyhftmitem20210721105823820.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIyhftmitem20210721105823820.png?Expires=1942196303&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=HAki8o%2B0O5jzQ3%2F%2BvGdU1Zd2oIs%3D" />上减函数,则<img id="PIpaaeeitem20210721105822214.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIpaaeeitem20210721105822214.png?Expires=1942196304&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=5tIpBbefKXm40vOZ0E%2BkjJgfTek%3D" />为( )
A.无界函数
B.L可测函数
C.不是几乎处处连续
D.绝对连续函数
答:————
10.[单选题] 若<img id="PIqsoovitem20210721105823614.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIqsoovitem20210721105823614.png?Expires=1942196303&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=TVs3QgDjt4bIY79vJmRcBSlxohY%3D" />,则( )
A.<img id="PIarowsitem20210721105824439.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIarowsitem20210721105824439.png?Expires=1942196304&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=DxQQbFFQayTCINvOLiO06gzHgDU%3D" />处处可导
B.<img id="PIalsplitem20210721105824668.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIalsplitem20210721105824668.png?Expires=1942196304&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=sOR2y16BGlHfkOg7P%2Be9nq0e8Kw%3D" />
C.<img id="PIherzvitem20210721105824806.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIherzvitem20210721105824806.png?Expires=1942196304&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=U8WG0I2Cmhjx5Djgt%2B%2FJKBdSujY%3D" />
D.<img id="PIrxxsqitem20210721105824986.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIrxxsqitem20210721105824986.png?Expires=1942196305&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=iF2VO97zf8VeK%2BnHhaGJZLSu7bM%3D" />处处连续
答:————
11.[单选题] 若A,B均为非空闭集,则( )
A.存在<img id="PImykpgitem20210721105823359.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PImykpgitem20210721105823359.png?Expires=1942196305&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=D%2BxPa%2BDOUrCBJ2kyi3wmhm9QSH0%3D" />
B.<img id="PIodfsyitem20210721105823524.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIodfsyitem20210721105823524.png?Expires=1942196303&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=LxxSzZrI5w4nApFCcgTHMMB7Fks%3D" />
C.存在不相交开集<img id="PIzytlcitem20210721105825471.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIzytlcitem20210721105825471.png?Expires=1942196305&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=B3Nk0xey94nU4Iv36hUE9e3teCE%3D" />
D.对任意<img id="PIuzhncitem20210721105825785.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIuzhncitem20210721105825785.png?Expires=1942196305&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=TyKaeD55RNhgQEOt0c9f2znger8%3D" />,存在<img id="PIogckwitem20210721105825843.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIogckwitem20210721105825843.png?Expires=1942196305&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=BizxS%2Fpq%2FRGaqGPWoO7i4t%2BdVdE%3D" />
答:————
12.[单选题] 在<img id="PIhzmkoitem20210721105825508.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIhzmkoitem20210721105825508.png?Expires=1942196306&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=32KZiNtJwt1tl5H4uH7j%2BxTEAZs%3D" />中,令<img id="PIruyibitem20210721105826371.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIruyibitem20210721105826371.png?Expires=1942196306&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=iVAIgl8ZlsQiYev83%2FsGqGNmZOk%3D" />,B是<img id="PIszubaitem20210721105826555.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIszubaitem20210721105826555.png?Expires=1942196306&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=bg3Imzvq4qaHsBhU90Bj8mDF0Gk%3D" />轴,则( )
A.A为有界闭集
B.B为有界闭集
C.<img id="PIyzpwzitem20210721105826681.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIyzpwzitem20210721105826681.png?Expires=1942196306&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=lD81poRlUd5Wz%2FIH3YN3AnSDduU%3D" />
D.<img id="PIhknqnitem20210721105826846.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIhknqnitem20210721105826846.png?Expires=1942196306&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=eCWRk0s4WW6EeLUfJTWijagIaRw%3D" />
答:————
13.[单选题] 在<img id="PIkvwbpitem20210721105827015.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIkvwbpitem20210721105827015.png?Expires=1942196306&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=LxdLI6gsjIg2Qf25ki7HAT3SgmI%3D" />中令<img id="PIynvbeitem20210721105826714.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIynvbeitem20210721105826714.png?Expires=1942196306&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=KIlscdhF%2BxBNaXUkkFBkI97qxSU%3D" />,<img id="PIelwsgitem20210721105826663.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIelwsgitem20210721105826663.png?Expires=1942196306&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=4V81bFM6q2ykhhKT8YKF7EbN9Yg%3D" />则( )
A.<img id="PIkfixtitem20210721105827476.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIkfixtitem20210721105827476.png?Expires=1942196307&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=qUY%2B1%2FyhQDXJSJtrlNdA9A7Uabg%3D" />
B.B为有界闭集
C.<img id="PIjlvuwitem20210721105827595.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIjlvuwitem20210721105827595.png?Expires=1942196307&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=HGMpDDYzt15Qr5X%2BQEHUtnCkHDk%3D" />
D.<img id="PIwrraoitem20210721105827613.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIwrraoitem20210721105827613.png?Expires=1942196307&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=fDLrGERTVW0asZxB51B%2FuzbGJrY%3D" />
答:————
14.[单选题] 设<img id="PIotivkitem20210721105827936.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIotivkitem20210721105827936.png?Expires=1942196308&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=7fQfcvfCYDMnMHplQzBxbrVCivg%3D" />在X上分别测度收敛于<img id="PIsgbykitem20210721105828111.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIsgbykitem20210721105828111.png?Expires=1942196308&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=tsUgLwEc9TTZlfC9vXCBgwvpujo%3D" />与<img id="PIwabrsitem20210721105827601.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIwabrsitem20210721105827601.png?Expires=1942196358&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=UDkI5Oz5XF5g5mQcX96SFUQeruY%3D" />,则( )
A.<img id="PIprvhcitem20210721105919087.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIprvhcitem20210721105919087.png?Expires=1942196359&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=pUlzNQ3xNB%2FIxJauijAx1B3AFw8%3D" />测度收敛于<img id="PIlttjxitem20210721105919375.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIlttjxitem20210721105919375.png?Expires=1942196359&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=tKcqKXBZVTIm8UoiLkSGhfwArsE%3D" />
B.<img id="PIswfhhitem20210721105919575.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIswfhhitem20210721105919575.png?Expires=1942196359&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=eA11nfaN5EnF3yHArG%2BsYm3pseA%3D" />测度收敛于<img id="PIdkeupitem20210721105919279.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIdkeupitem20210721105919279.png?Expires=1942196359&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=TpcZ7gryqsuBN65FgA80R6A3VV0%3D" />
C.<img id="PIiekinitem20210721105919228.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIiekinitem20210721105919228.png?Expires=1942196359&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=ireMGaAeSgfA6MgfUlLT32VGhCs%3D" />测度收敛于<img id="PIrgnwyitem20210721105919593.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIrgnwyitem20210721105919593.png?Expires=1942196360&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=JdObmPv9rhC3IxiRh8XRAHw3a4M%3D" />
D.<img id="PIetykgitem20210721105919764.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIetykgitem20210721105919764.png?Expires=1942196360&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=DDa3SlvjHbVm5nybj6P%2F4g4EcDw%3D" />测度收敛于<img id="PIcaggwitem20210721105919698.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIcaggwitem20210721105919698.png?Expires=1942196360&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=DD00h3kuygyhi5UxymQ1Xwa96q8%3D" />
答:————
15.[单选题] 在<img id="PIutcghitem20210721105920502.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIutcghitem20210721105920502.png?Expires=1942196360&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=sazcDO4EzAmooqWnLCG1pOwm0dk%3D" />上定义<img id="PIkzekuitem20210721105920644.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIkzekuitem20210721105920644.png?Expires=1942196360&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=R03Quy5wLPgNPJruXQLJh5MDkEo%3D" />,当<img id="PIufaiqitem20210721105920793.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIufaiqitem20210721105920793.png?Expires=1942196360&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=WNDBB5zfg8GMBJ4DBWN3qrjZhv0%3D" />为有理数时,<img id="PImszvwitem20210721105920324.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PImszvwitem20210721105920324.png?Expires=1942196360&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=ap46tmzSAuEDllV2JpaH8%2FVM4xU%3D" />,当<img id="PIjhkbwitem20210721105921181.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIjhkbwitem20210721105921181.png?Expires=1942196361&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=IIQE%2BfXDOWxalD1FvV11HdX0FIQ%3D" />为无理数时,<img id="PImlnwaitem20210721105921381.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PImlnwaitem20210721105921381.png?Expires=1942196361&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=GIGqzJdeLisT2OkUBCx45rFBAdU%3D" />,则( )
A.<img id="PIbukqsitem20210721105921577.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIbukqsitem20210721105921577.png?Expires=1942196361&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=mSfLdvWC8w3yBzYa0LWRWbkEUbk%3D" />在<img id="PIfxiolitem20210721105921751.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIfxiolitem20210721105921751.png?Expires=1942196361&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=6kO2fmJ2CVzyR1QBcSbfhTwEpso%3D" />上处处连续
B.<img id="PIzgpypitem20210721105921967.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIzgpypitem20210721105921967.png?Expires=1942196362&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=oh7v9Qj%2BUDjY%2BT3rGqffYSqNoFM%3D" />在<img id="PIfifyoitem20210721105921670.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIfifyoitem20210721105921670.png?Expires=1942196362&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=qVreG87puKK9y8P4l0sFQDX5sKA%3D" />上为L可测函数
C.<img id="PIibuzlitem20210721105922279.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIibuzlitem20210721105922279.png?Expires=1942196361&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=OIpQVHA4H5Qu7yRhA38PjFYr4Ck%3D" />在<img id="PIfjcjoitem20210721105922043.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIfjcjoitem20210721105922043.png?Expires=1942196362&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=M0DDWuEn5DAKu0HTlscGOJjU9mI%3D" />上几乎处处连续
D.<img id="PIcnhmmitem20210721105922659.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIcnhmmitem20210721105922659.png?Expires=1942196362&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=jFqeNIZogvAt7%2Fdo%2FlxgpmfbpSg%3D" />在<img id="PIlzmhfitem20210721105922351.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIlzmhfitem20210721105922351.png?Expires=1942196362&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=1TkC10GK%2FYRqqKzeerO%2Ffd5OAE8%3D" />上不是L可积函数
答:————
16.[单选题] 当<img id="PIfhkiditem20210721105922994.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIfhkiditem20210721105922994.png?Expires=1942196362&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=359ZlwQ0TuT6S72XPG42a1bUVvI%3D" />,则( )
A.<img id="PIggqwuitem20210721105923133.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIggqwuitem20210721105923133.png?Expires=1942196363&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=9j%2F%2FfQeQEIMIiHMvMCwC6MqQC%2BE%3D" />连续
B.<img id="PIzkznritem20210721105923295.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIzkznritem20210721105923295.png?Expires=1942196361&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=T%2FpioJk1%2FicNMQL1WUUKD%2F%2F86kQ%3D" />
C.<img id="PIerhjbitem20210721105923287.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIerhjbitem20210721105923287.png?Expires=1942196363&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=HA2oQfS%2FFn5XKs869sk2d5MR%2BBA%3D" />
D.<img id="PIpqstvitem20210721105923114.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIpqstvitem20210721105923114.png?Expires=1942196363&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=fVuA3zvMPxP8M01Um9hZ6P72m1o%3D" />
答:————
17.[单选题] 若<img id="PItlmzfitem20210721105921831.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PItlmzfitem20210721105921831.png?Expires=1942196363&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=TcDst4IrkXte3VfZRaaI6a62aqY%3D" />,则( )
A.<img id="PIrtluwitem20210721105923468.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIrtluwitem20210721105923468.png?Expires=1942196363&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=c3g1NYeRSLbLrqx5Ca6eSWJrcv0%3D" />
B.<img id="PIrhxutitem20210721105924315.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIrhxutitem20210721105924315.png?Expires=1942196364&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=ANonzbTvwwL%2FrDfnri5Sz9vXzjE%3D" />
C.<img id="PIwstveitem20210721105924477.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIwstveitem20210721105924477.png?Expires=1942196364&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=yY8u7AoAYA%2B9gnhKbbviOfhi0ao%3D" />
D.当A或C之一为无限集时,<img id="PIpxcmuitem20210721105924713.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIpxcmuitem20210721105924713.png?Expires=1942196364&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=d2IAEoHnNBwcPQtHmmGApIEbfrc%3D" />
答:————
18.[单选题] 设E为<img id="PIqmyeeitem20210721105925023.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIqmyeeitem20210721105925023.png?Expires=1942196365&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=gpXfMSjkfBthS%2F6%2FYRwBsfPBI%2FM%3D" />中的一个不可测集,令<img id="PIrdrwxitem20210721105925289.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIrdrwxitem20210721105925289.png?Expires=1942196365&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=Ap2F79DPPQ6LIy4%2FBwtNJWECUCs%3D" />,则<img id="PIlfnqxitem20210721105924799.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIlfnqxitem20210721105924799.png?Expires=1942196365&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=Q6FH81tGBCgRT6sBeXkKp1PMIHk%3D" />必是( )
A.L可测函数
B.L可积函数
C.有界函数
D.连续函数
答:————
19.[问答题] 设<img id="PIsogmuitem20210721105925164.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIsogmuitem20210721105925164.png?Expires=1942196365&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=3QOCI3NqlA3ZQgMawKg2OKl8QEg%3D" />,<img id="PIaipwzitem20210721105925306.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIaipwzitem20210721105925306.png?Expires=1942196366&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=gp42%2FH%2Fy%2FcIyL%2FMmGKSh9rqXoCs%3D" /><img id="PIhfvduitem20210721105925447.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIhfvduitem20210721105925447.png?Expires=1942196366&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=nGYedd8670bMUTMVhFJ%2Brte8mOk%3D" /><img id="PIouxflitem20210721105926259.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIouxflitem20210721105926259.png?Expires=1942196366&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=PjJF6cxeYiHZP78w2COzTKmPefM%3D" />是互不相交的闭集,则有互不相交的开集<img id="PIkdxkgitem20210721105926454.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIkdxkgitem20210721105926454.png?Expires=1942196366&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=K0CqDCP37BGTJuJ8OXWGnQl4joE%3D" />,<img id="PIxaprzitem20210721105926602.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIxaprzitem20210721105926602.png?Expires=1942196366&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=zZhKZBi7%2BNBRsk%2By6iP1wXgw9x0%3D" />使<img id="PIcufdpitem20210721105926761.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIcufdpitem20210721105926761.png?Expires=1942196364&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=FSMLMWy5LwZ73CIac%2FUBKxKUn9s%3D" /><img id="PIhydpeitem20210721105926956.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIhydpeitem20210721105926956.png?Expires=1942196366&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=w8RF%2Btm3bua706uyW52PyftrJbQ%3D" /><img id="PIzszciitem20210721105927121.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIzszciitem20210721105927121.png?Expires=1942196367&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=68IZrIPk%2FfFRFVcve9SS2zCjex8%3D" />,<img id="PItgkdgitem20210721105927311.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PItgkdgitem20210721105927311.png?Expires=1942196367&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=CLZwk4hvLnqRvjw5OWljI3cLITk%3D" /><img id="PIzlkmoitem20210721105927612.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIzlkmoitem20210721105927612.png?Expires=1942196365&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=KIeGuMJ%2FuZyxlSnQA2FPlAztE%2FM%3D" /><img id="PIujfdkitem20210721105927774.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIujfdkitem20210721105927774.png?Expires=1942196367&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=fhgCL04eBGZsbPkZw9fUNrzJLG4%3D" />.
答:————
20.[问答题] 设<img id="PItaqsiitem20210721105930858.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PItaqsiitem20210721105930858.png?Expires=1942196371&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=UshnD99h7P1EKjM%2B3idE%2Fq%2Ba0Dg%3D" /><img id="PIunocritem20210721105930656.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIunocritem20210721105930656.png?Expires=1942196369&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=WgsDF0ldnyHiyNxL5gYk3%2BmGZUA%3D" /><img id="PIikvggitem20210721105931257.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIikvggitem20210721105931257.png?Expires=1942196370&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=zJv5XEUcG6u93z%2FnllzhlhBIXqY%3D" />,则有区间<img id="PIxhdytitem20210721105931433.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIxhdytitem20210721105931433.png?Expires=1942196371&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=X4dDgZXKEWaNJL2IBabQBOt8uuQ%3D" />,使得<img id="PIamzcgitem20210721105931653.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIamzcgitem20210721105931653.png?Expires=1942196369&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=6z2n%2FYMy%2BVezJYGdEbOZ1P5iDrg%3D" /> <img id="PIctelwitem20210721105931343.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIctelwitem20210721105931343.png?Expires=1942196369&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=e7CEZk8T2jfWbl9Vm1UwsPBZbAU%3D" /><img id="PItsxzditem20210721105931945.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PItsxzditem20210721105931945.png?Expires=1942196372&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=uyl0iFrsTctyC59aaGutRrl8IPI%3D" /><img id="PIymzfaitem20210721105931967.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIymzfaitem20210721105931967.png?Expires=1942196372&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=00wywLEGnu6oeYp0aRZ%2B0DXZWpE%3D" />(<img id="PIfpbelitem20210721105932161.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIfpbelitem20210721105932161.png?Expires=1942196372&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=iRDx3DTUZ7RuP5R6HbarSFL5CMU%3D" />).
答:————
21.[问答题] 设<img id="PIvnyzwitem20210721105936797.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIvnyzwitem20210721105936797.png?Expires=1942196378&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=o6X6u1J8B7Fl2ZovMVB1AU9qT84%3D" />则对任何可测集<img id="PIazrebitem20210721105938895.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIazrebitem20210721105938895.png?Expires=1942196378&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=4oG%2BhKA5jiwx%2BnyzCfuR%2B5ICujc%3D" />有<img id="PIerxwcitem20210721105938401.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIerxwcitem20210721105938401.png?Expires=1942196378&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=bm3Dh%2BbBWSzHzUh25EuC55HbXpI%3D" />
答:————
22.[问答题] 设<img id="PIubbktitem20210721105942129.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIubbktitem20210721105942129.png?Expires=1942196382&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=%2FezJe0o9NgSDcWofYW%2Fc3uaBfNk%3D" /><br>则<img id="PIggiceitem20210721105941781.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIggiceitem20210721105941781.png?Expires=1942196382&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=MyZ35L8feGx5CMwlro%2FZUDk5k1w%3D" />且<img id="PIqgsbhitem20210721105942931.png" src="https://oescdn.open.com.cn/zyglpt/PI/item/2021/0721/PIqgsbhitem20210721105942931.png?Expires=1942196383&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=Je90mx3pYWIICm64QVjaUpM8wrc%3D" />
答:————
23.[问答题] 简述Lebesgue积分与Riemann积分的区别与联系
答:————
24.[问答题] 叙述直线上非空开集的结构,并简述康托尔集(Cantor)的主要性质.
答:————
25.[问答题] 简述可测函数列的四种收敛性(处处收敛、几乎处处收敛、一致收敛、测度收敛)之间的关系
答:————
页:
[1]