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Probability measure functors preserving the ANR-property of metric spaces


Authors: Nguyen To Nhu and Ta Khac Cu
Journal: Proc. Amer. Math. Soc. 106 (1989), 493-501
MSC: Primary 60B05; Secondary 46E27, 54C55
DOI: https://doi.org/10.1090/S0002-9939-1989-0964459-9
MathSciNet review: 964459
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Abstract: Let $ {P_k}\left( X \right)$ denote the set of all probability measures on a metric space $ X$ whose supports consist of no more than $ k$ points, equipped with the Fedorchuk topology. We prove that if $ X \in {\text{ANR}}$ then $ {P_k}\left( X \right) \in {\text{ANR}}$ for every $ k \in {\mathbf{N}}$. This implies that for each $ k \in {\mathbf{N}}$ the functor $ {P_k}$ preserves the topology of separable Hilbert space.


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DOI: https://doi.org/10.1090/S0002-9939-1989-0964459-9
Keywords: ANR, probability measure, Hilbert space
Article copyright: © Copyright 1989 American Mathematical Society

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