The topology of spaces of probability measures, I

Taras Banakh

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arXiv · 1112.6161

The topology of spaces of probability measures, I

Taras Banakh

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Abstract

For a Tychonoff space $X$, the constructions $\hat P(X)$ and $P_τ(X)$ of the spaces of probability Radon measures and probability $τ$-smooth measures on $X$ are considered. It is proved that these constructions determine functors in the category of Tychonoff spaces, which extend the functor $P$ of probability measures in the category of compacta. In this part we investigate general topological properties of the spaces $\hat P(X)$ and $P_τ(X)$, as well as categorial properties of the functors $\hat P$ and $P_τ$.

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Taras Banakh. 2016-02-19. The topology of spaces of probability measures, I. https://arxiv.org/abs/1112.6161

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