| 函数的可测性问题 |
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| 引用本文： | 刘晓鹏,赵生变.函数的可测性问题[J].数学的实践与认识,2004,34(12):154-161. |
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| 作者姓名： | 刘晓鹏 赵生变 |
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| 作者单位： | 北京交通大学理学院,北京,100044 |
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| 摘 要： | 讨论了函数的可测性问题 ,特别是函数的 Borel可测和 Lebesgue可测的关系 .对相应结论给出了明确和严格的证明 .利用本文的结果 ,我们严格证明了 Lebesgue积分的变量替换公式 .此外还明确指出了分布函数密度的等价唯一性问题 .
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| 关 键 词： | Borel可测 Lebesgue可测 Lebesgue积分 |
| 修稿时间： | 2003年7月18日 |
The Measurability of Function |
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| LIU Xiaopeng,ZHAO Shengbian.The Measurability of Function[J].Mathematics in Practice and Theory,2004,34(12):154-161. |
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| Authors: | LIU Xiaopeng ZHAO Shengbian |
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| Abstract: | This paper discusses the problems about measurability of function, especially, the relations between Borel measurability and Lebesgue measurability of functions. Besides, the specific and strict proofs of the relevant conclusions are given. We prove the variable replacement formula of Lebesgue integration strictly by using solutions of this paper, and demonstrate the problems of equivalence and uniqueness about denisty of distribution function definitely. |
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| Keywords: | Borel measurable lebesgue measurable lebesgue integration |
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