A note on the Gauss-Green theorem
A note on the Gauss-Green theorem
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关于高斯-格林定理的注释
DOI：
10.1090/s0002-9939-1958-0095245-2
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发表时间：
1958
影响因子：
1.3
通讯作者：
H. Fédérer
中科院分区：
文献类型：
--
作者：
H. Fédérer
最近，De Giorgi在[DG 1]和[DG 2]中研究了高斯-格林公式（n空间）的一个非常一般的测量理论版本。Fleming和Young在[FY]中使用“广义曲面”技术，独立地获得了相关的结果（对于3-空间）。在这里，De Giorgi的作品将通过使用在[f1]中引入的外法线的几何概念来补充。假设A是欧几里得n空间E的一个子集，相对于Lebesgue测度L可测量，考虑以下两个条件：(1)存在有限的实值（有符号）Borel测度(D, *,n / E，使得
A very general measuretheoretic version of the Gauss-Green formula (for n-space) has recently been studied by De Giorgi in [DG 1 ] and [DG 2]. Independently Fleming and Young have obtained related results (for 3-space) in [FY], employing the technique of "generalized surfaces." Here the work of De Giorgi will be supplemented through use of the geometric concept of exterior normal introduced in [F 1]. Assuming that A is a subset of Euclidean n-space E, measurable with respect to Lebesgue measure L, consider the following two conditions: (1) There exist finite real valued (signed) Borel measures (D, * ,n over E. such that