鲁金定理与可测函数的本性定理

Lusin Theorem and the Natural Disposition Theorem of the Measurable Functions

讨论鲁金定理与勒贝格可测函数的本性定理之间的关系,利用n-维勒贝格可测集几乎所有的点都是全密点与鲁金定理的结论证明勒贝格可测函数的本性定理,利用勒贝格可测函数的本性定理证明鲁金定理。

The relations between the Lusin theorem and the natural disposition theorem of the Lebesgue measurable functions are discussed in this paper, according to the almost every point of the n-dimension Lebesgue measurable set being the entire dense spot and the Lusin theorem. The natural disposition theorem of Lebesgue measurable functions is proved, and so is the Lusin theorem by the natural disposition theorem of the Lebesgue measurable functions.