变差函数与测度中的某些问题

Some Problems About Variational Function and Measure

变差函数为数学研究中涉及较多的内容,特别是在与测度有关的研究中.本文明确指出了变差函数的全变差与生成测度之间的关系,并给出了严格的证明.此外,还讨论了测度与积分的一些性质,相应结论亦作了详尽推证.

Variational function is frequently touched upon in mathematic researches, especially in researches relative to measure. This paper points out the relation between total variation of variational function and generated measure definitely, and gives the strict proof. Besides, this paper discusses some properties of measure and integration, and proves thoroughly the relevant conclusions.