Some Topological Properties of the Space of Probability Measures

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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