The topology of spaces of probability measures, I

Abstract

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 $P_{\tau }$.

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

Cited by in corpus (1)

• Spaces of measurable functions