Geodesic
On compactification of spaces of measures
Funkcionalʹnyj analiz i ego priloženiâ, Tome 58 (2024) no. 1, pp. 4-21

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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.
Keywords: Radon measure, weak topology, Stone–Čech compactification, compactification of the space of measures.
Mots-clés : Samuel compactification 
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     author = {Vladimir Bogachev},
     title = {On compactification of spaces of measures},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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     publisher = {mathdoc},
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     number = {1},
     year = {2024},
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     url = {http://geodesic.mathdoc.fr/item/FAA_2024_58_1_a1/}
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Vladimir Bogachev. On compactification of spaces of measures. Funkcionalʹnyj analiz i ego priloženiâ, Tome 58 (2024) no. 1, pp. 4-21. http://geodesic.mathdoc.fr/item/FAA_2024_58_1_a1/