Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Extension of random contractions

Authors: J. Myjak and W. Zygadlewicz
Journal: Proc. Amer. Math. Soc. 103 (1988), 951-955
MSC: Primary 54C20; Secondary 28B20, 47H09
MathSciNet review: 947689
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Abstract: Let $ \Omega $ be a measurable space. Let $ X$ and $ Y$ be separable Hilbert spaces and let $ D$ be a subset of $ X$. Then every random contraction $ f:\Omega \times D \to Y$ can be extended to a random contraction defined on all $ \Omega \times X$. This statement remains true if $ \Omega $ is a complete measurable space, $ X$ and $ Y$ are separable metric spaces and the pair $ (X,Y)$ has the Kirszbraun intersection property.

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Keywords: Random contraction, random isometry, extension, multifunction, measurable selection, separable metric space, Hilbert space
Article copyright: © Copyright 1988 American Mathematical Society