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This article is cited in 10 scientific papers (total in 10 papers)
Topology of spaces of probability measures
T. O. Banakh, T. N. Radul Ivan Franko National University of L'viv
Abstract:
We study the space $\widehat P(X)$ of Radon probability measures on a metric space $X$ and its subspaces $P_c(X)$, $P_d(X)$ and $P_\omega (X)$ of continuous measures, discrete measures, and finitely supported measures, respectively. It is proved that for any completely metrizable space $X$, the space $\widehat P(X)$ is homeomorphic to a Hilbert space. A topological classification is obtained for the pairs $(\widehat P(K),\widehat P(X))$,
$(\widehat P(K),P_d(Y))$ and $(\widehat P(K),P_c(Z))$, where $K$ is a metric compactum, $X$ an everywhere dense Borel subset of $K$, $Y$ an everywhere dense $F_{\sigma \delta }$-set of $K$, and $Z$ an everywhere uncountable everywhere dense Borel subset of $K$ of sufficiently high Borel class. Conditions on the pair $(X,Y)$ are found that are necessary and sufficient for the pair $(\widehat P(X),P_\omega (Y))$ to be homeomorphic to $(l^2(A),l^2_f(A))$.
Received: 30.10.1995
Citation:
T. O. Banakh, T. N. Radul, “Topology of spaces of probability measures”, Sb. Math., 188:7 (1997), 973–995
Linking options:
https://www.mathnet.ru/eng/sm241https://doi.org/10.1070/sm1997v188n07ABEH000241 https://www.mathnet.ru/eng/sm/v188/i7/p23
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Abstract page: | 843 | Russian version PDF: | 482 | English version PDF: | 82 | References: | 101 | First page: | 1 |
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