Some Topological Properties of the Space of Probability Measures
Lobachevskii Journal of Mathematics(2023)
摘要
In this work, the separability, locally separability, weakly separability and locally weakly separability of the space of probability measures of an infinite compact space are studied. It is proved that an infinite compact space X is a separable (locally separable), if and only if the space P_n(X) is a separable (locally separable). It was also proved that, if a space X is a weakly separable (locally weakly separable), then the space P_n(X) is a weakly separable (locally weakly separable).
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关键词
separability,locally separability,weakly separability,locally weakly separability,probability measure
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