概率测度空间$P_f(X)$的几何性质
Geometrical properties of the space $P_f(X)$ of probability measures
摘要：
本文证明了对紧空间$X$包含$P_{f}(X)\in ANR$成立当且仅当$X\in ANR$成立.进一步证明了函子$P_{f}$保持紧致的性质为$Q$ -流形或Hilbert立方体，映射纤维的性质为$ANR$ -紧致，$Q$ -流形，Hilbert立方体（Hilbert立方体的有限）.
英文摘要：
In this paper we prove that for a compact space $X$ inclusion $P_{f}(X)\in ANR$ holds if and only if $X\in ANR$. Further, it is shown that the functor $P_{f}$ preserves property of a compact to be $Q$-manifold or a Hilbert cube, properties of maps fibres to be $ANR$-compact, $Q$-manifold, Hilbert cube (the finite of Hilbert cube).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
