Compactification of Spaces of Measures and Pseudocompactness

IF 0.5 4区数学 Q3 MATHEMATICS

Doklady Mathematics Pub Date : 2024-09-29 DOI:10.1134/S1064562424702181

V. I. Bogachev

引用次数: 0

Abstract

We prove pseudocompactness of a Tychonoff space X and the space \(\mathcal{P}(X)\) of Radon probability measures on it with the weak topology under the condition that the Stone–Čech compactification of the space \(\mathcal{P}(X)\) is homeomorphic to the space \(\mathcal{P}(\beta X)\) of Radon probability measures on the Stone–Čech compactification of the space X.

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度量空间的紧凑性与伪紧凑性

在空间 \(\mathcal{P}(X)\ 的 Stone-Čech compactification 与空间 X 的 Stone-Čech compactification 上的 Radon 概率度量的空间 \(\mathcal{P}(\beta X)\)同构的条件下，我们证明了弱拓扑的 Tychonoff 空间 X 及其上的 Radon 概率度量的空间 \(\mathcal{P}(X)\ 的伪紧密性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Doklady Mathematics 数学-数学

CiteScore

1.00

自引率

16.70%

发文量

审稿时长

3-6 weeks

期刊介绍： Doklady Mathematics is a journal of the Presidium of the Russian Academy of Sciences. It contains English translations of papers published in Doklady Akademii Nauk (Proceedings of the Russian Academy of Sciences), which was founded in 1933 and is published 36 times a year. Doklady Mathematics includes the materials from the following areas: mathematics, mathematical physics, computer science, control theory, and computers. It publishes brief scientific reports on previously unpublished significant new research in mathematics and its applications. The main contributors to the journal are Members of the RAS, Corresponding Members of the RAS, and scientists from the former Soviet Union and other foreign countries. Among the contributors are the outstanding Russian mathematicians.