On compactification of spaces of measures

Vladimir Bogachev

Funkcionalʹnyj analiz i ego priloženiâ, Tome 58 (2024) no. 1, pp. 4-21.

Résumé

In this paper, we compare the Stone–Čech compactification $\beta \mathcal{P}(X)$ of the space $\mathcal{P}(X)$ of Radon probability measures on a Tychonoff space $X$, equipped with the weak topology, with the space $\mathcal{P}(\beta X)$ of Radon probability measures on the Stone–Čech compactification $\beta X$ of the space $X$. It is shown that for any noncompact metric space $X$, the compactification $\beta \mathcal{P}(X)$ does not coincide with $\mathcal{P}(\beta X)$. We discuss the case of more general Tychonoff spaces and also the case of the Samuel compactification, for which the coincidence holds.

Détail

Keywords: Radon measure, weak topology, Stone–Čech compactification, compactification of the space of measures.
Mots-clés : Samuel compactification

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