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单选题 设是闭区间中的无理点集,则( )

A. 是闭集

B. 是不可测集

C.

D.

实变函数课程封面

学科：实变函数

时间：2024-07-15 15:47:58

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题目1
单选题
设<img src="https://tihai-oss-cloud.itihey.com/img/f7097a7ed5e868c87c40e8849f7ee06e.png">是一列递增集合,<img src="https://tihai-oss-cloud.itihey.com/img/11fb672ad26c568c948ecbbc1a042403.png">,则<img src="https://tihai-oss-cloud.itihey.com/img/d82597523a239f8dc62d262d1a370023.png">与<img src="https://tihai-oss-cloud.itihey.com/img/b65a28cc29298ec1f6f96d110dc20d9f.png">的外测度满足( )
A. <img src="https://tihai-oss-cloud.itihey.com/img/dfab0542cae6102f2e0de130fd2dcca2.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/13ff85c8d0f40eb488ea36cba9c165f6.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/d6e5fb5b5a9e21f64c3a25e94279e50f.png">D. 不能比较
题目2
单选题
设<img src="https://tihai-oss-cloud.itihey.com/img/7343d77eb43f8085533876edb4826a4d.png">是一列可测集,<img src="https://tihai-oss-cloud.itihey.com/img/c2040be6893f649e67937ec36a4f7e71.png">,则有( )
A. <img src="https://tihai-oss-cloud.itihey.com/img/f715f9246adbf85b3b12a453511bef6f.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/00156353c74ec16fe69d166ee03530b9.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/6f53d489e206f02cfc4bb0b3b4b467b9.png">D. 以上都不对
题目3
单选题
设<img src="https://tihai-oss-cloud.itihey.com/img/09373240cef51e41469aafd9ae709a47.png">是闭区间<img src="https://tihai-oss-cloud.itihey.com/img/2c9cfa71c1ba9d7061dfedd1fd36d9cb.png">中的无理点集,则( )
A. <img src="https://tihai-oss-cloud.itihey.com/img/09373240cef51e41469aafd9ae709a47.png">是闭集B. <img src="https://tihai-oss-cloud.itihey.com/img/09373240cef51e41469aafd9ae709a47.png">是不可测集C. <img src="https://tihai-oss-cloud.itihey.com/img/64ac1acea3bbb6ac8e020fefa80d40b8.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/7923c19e6ee0809d3767c27da90b0176.png">
题目4
单选题
设E是R中无理数全体,则mE( )
A. 0B. 1C. +&infin;D. -&infin;
题目5
单选题
下列说法不正确的是( )
A. 凡外侧度为零的集合都可测B. 可测集的任何子集都可测C. 开集和闭集都是波雷耳集D. 波雷耳集都可测
题目6
单选题
下列说法不正确的是( )
A. 若<img src="https://tihai-oss-cloud.itihey.com/img/39e211d795b7512a8087f189e784ca1c.png">,则<img src="https://tihai-oss-cloud.itihey.com/img/ebfb1347b95721670061a48bf18a63a9.png">B. 可测集的任何子集都可测C. 凡开集、闭集皆可测D. 有限个或可数个零测度集之和集仍为零测度集
题目7
单选题
下列断言中( )是错误的
A. 零测集是可测集B. 可数个零测集的并是零测集C. 任意个零测集的并是零测集D. 零测集的任意子集是可测集
题目8
单选题
设<img src="https://tihai-oss-cloud.itihey.com/img/09373240cef51e41469aafd9ae709a47.png">是<img src="https://tihai-oss-cloud.itihey.com/img/8a09469cc997522b629e3aee861b9fce.png">中点集,如果对任一点集<img src="https://tihai-oss-cloud.itihey.com/img/437f786c1a8578995eded8e192761ee6.png">都有____,则称<img src="https://tihai-oss-cloud.itihey.com/img/09373240cef51e41469aafd9ae709a47.png">是<img src="https://tihai-oss-cloud.itihey.com/img/f838aba671fa372aebe1d08ad13ad7c0.png">可测的
A. <img src="https://tihai-oss-cloud.itihey.com/img/a70d1e1d30a10487279579fcb442b61c.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/c6dde795277b1165a7823983d860ab9d.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/3922b87a7eaf83fa1c2422f932fa73b3.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/b650956b383c79462dad54351936926d.png">
题目9
单选题
设<img src="https://tihai-oss-cloud.itihey.com/img/3fdf564d397f656c90c3de3f8dd1ede1.png">,则<img src="https://tihai-oss-cloud.itihey.com/img/695d6a8ad643b0c62fa834ec5c6b3bb8.png">=____
A. 0B. 2C. 1D. 4
题目10
单选题
设<img src="https://tihai-oss-cloud.itihey.com/img/09373240cef51e41469aafd9ae709a47.png">是[0,1]中无理数全体,则<img src="https://tihai-oss-cloud.itihey.com/img/695d6a8ad643b0c62fa834ec5c6b3bb8.png">=____
A. 0B. 1C. 2D. 3
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