Compactification of spaces of measures and pseudocompactness

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Abstract

We prove pseudocompactness of a Tychonoff space X and the space P(X) of Radon probability measures on it with the weak topology under the condition that the Stone–ech compactification of the space P(X) is homeomorphic to the space P(βX) of Radon probability measures on the Stone–ech compactification of the space X.

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About the authors

V. I. Bogachev

Moscow State Lomonosov University; National Research University Higher School of Economics; Saint-Tikhon's Orthodox University; Moscow Center of Fundamental and Applied Mathematics

Author for correspondence.
Email: vibogach@mail.ru

Corresponding Member of the RAS

Russian Federation, Moscow; Moscow; Moscow; Moscow

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