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 .
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.
出处
《数学的实践与认识》
CSCD
北大核心
2004年第12期154-161,共8页
Mathematics in Practice and Theory
