n-维可测函数的本性定理

The natural disposition theorem on n-dimension measurable function

将一维勒贝格可测集的全密点定义推广到n-维可测集,将一维空间的函数间断度概念、相对间断度概念推广到n-维空间;根据全密点定义,利用n-维维他利覆盖定理与鲁金定理直接证明`n-维勒贝格可测集几乎所有的点都是全密点;由函数间断度与相对间断度概念得到n-维勒贝格可测函数与一个几乎处处连续的函数几乎处处相等的结论.

The definition of the entire dense spot of Lebesgue measurable set was generalized from 1- dimension to n-dimension, so did the concept of the degree and the relative degree of the discontinuity of function, according to the definition of the entire dense spot, the almost every point of n -dimension Lebesgue measurable set being the entire dense spot was directly proved by Vitali cover and Lusin theorem, that ndimension Lebesgue measurable function was almost everywhere equal to an almost everywhere continuous function, which was gotten by the conception of the degree and the relative degree of the discontinuity of function.