关于乘积Loeb空间上的集合泛可测性的若干结果

Some Results of Universal Loeb-mcasurability of Sets in Product Loeb Space

本文将文[1]关于集合泛Locb可测性的讨论推广到乘积Locb空间上进行,得到了若干乘积泛Locb可测集的性质定理,在给定的k-饱和的非标准模型中,我们主要证明了Lu（·B1）×Lu（·B2） Lu（·B1×·B2）以及若干外集Rns,μ（Ω）,μ（X1,X2）和对角线集△是乘积泛Locb可测集。

In this paper, by using the theory and method in (1), the author discuss the universal measurability of sets in product Loeb space. It is shown that and for a k-sturat ed models, many external sets of nonstandard analysis-such as Rn3, μ(Ω), μ(x1×x2) and Δ-set are product universal Loeb-measurable, i. e. Loeb-measurable with respect to every internal product measure.