The topology of spaces of probability measures, I

Details The topology of spaces of probability measures, I The topology of spaces of probability measures, I

2011-12-28

arxiv.org/abs/1112.6161v1

Mat. Studii. 5 (1995) 65-87

Mathematics

General Topology

23 pages. This text is English translation (made by Oles potyatynyk) of the Russian original paper from 1995

Scientific paper

For a Tychonoff space $X$, the constructions $\hat P(X)$ and $P_\tau(X)$ of the spaces of probability Radon measures and probability $\tau$-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 $P_\tau(X)$, as well as categorial properties of the functors $\hat P$ and $P_\tau$.

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