Continuous selections as parametrically defined integrals

被引：0

作者：

P. V. Semenov

机构：

[1] Moscow City Pedagogical University,Department of Mathematics

来源：

Functional Analysis and Its Applications | 2008年 / 42卷

关键词：

continuous selection; convex-valued map; non-locally-convex vector space; paracompact space; probability measure;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

An analog of the classical Michael theorem on continuous single-valued selections of lower semicontinuous maps whose values are closed and convex in a Fréchet space is proved for maps into metrizable (non-locally-convex) vector spaces. It turns out that, instead of the local convexity of the whole space containing these values, it is sufficient to require that the family of values of the map be uniformly locally convex. In contrast to the standard selection theorems, the proof bypasses the process of successively improving the approximations, and the desired selection is constructed as the result of pointwise integration with respect to a suitable probability distribution.

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