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This article is cited in 9 scientific papers (total in 9 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”, Mat. Sb., 188:7 (1997), 23–46; 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: | 799 | Russian version PDF: | 464 | English version PDF: | 66 | References: | 91 | First page: | 1 |
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