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 Funktsional. Anal. i Prilozhen.: Year: Volume: Issue: Page: Find

 Funktsional. Anal. i Prilozhen., 2008, Volume 42, Issue 2, Pages 89–94 (Mi faa2908)

Brief communications

Continuous Selections as Parametrically Defined Integrals

P. V. Semenov

Moscow City Pedagogical University, Mathematical Department

Abstract: 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 \del{pointwise} 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.

Keywords: continuous selection, convex-valued map, non-locally-convex vector space, paracompact space, probability measure

DOI: https://doi.org/10.4213/faa2908

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English version:
Functional Analysis and Its Applications, 2008, 42:2, 155–159

Bibliographic databases:

UDC: 515.12+517.982.252

Citation: P. V. Semenov, “Continuous Selections as Parametrically Defined Integrals”, Funktsional. Anal. i Prilozhen., 42:2 (2008), 89–94; Funct. Anal. Appl., 42:2 (2008), 155–159

Citation in format AMSBIB
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