摘要
设(X,T)是Hausdorff拓扑空间,(X,A)是内可测空间,v是A上的有限内容度。本文利用非标准分析方法,给出了X上的Borel集在标准部分映射下的原象关于A Loeb可测的一个条件,对每一T∈T,有T∈L(v,A),并且对每一ε∈R^+,存在紧集C(?)T,使得L(v)(T-C)<ε。并进一步利用v的Loeb测度,构造出了X上的Radon测度L(v)·ST^(-1)。
Let (X,T) be a topological space, (~* X,A) be an internal measurable space, v be an internal finite content on A. a condition is giver for Loeb measurability of st^(-1) (B) with respect to A, where B is a Borel subset of X. That is: for each T∈T, ~*T∈L(v,A), and for each ε∈R^+, there is a compact subset CT, so L(v(~* T-~* C<ε. Forthmore, a Radon measure is constructed on X from the Loeb measure of v.
出处
《陕西师大学报（自然科学版）》
CSCD
1992年第4期14-17,共4页
Journal of Shaanxi Normal University(Natural Science Edition)
关键词
非标准分析
测度
Loeb
RADON
nonstandard analysis
nonstandard model
standard part map
