连续可微变换与可测集及可测函数

摘要

This paper discusses the problems about continuously differentiable transformation and Lebesgue measurability of set and functions.Besides,the specific and strict proofs of the relevant conclusion are given.We prove the variable replacement formula of Lebesgue itegration strictly by using solutions of this paper.%讨论了连续可微的一一变换下,集合与函数的Lebesgue可测性问题,对相应结论给出了简明而严格的证明,利用文中结果证明了Lebesgue积分的变量替换公式。