Regularity properties of measures on compact spaces
Regularity properties of measures on compact spaces
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紧空间测度的正则性质
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
M. Krupski
中科院分区：
文献类型：
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作者：
M. Krupski
证明了概率空间Radon测度的一个新的二分性定理。给出了这一结果的一些应用。本文研究了紧空间上的测度的一些性质。我们证明了紧空间上概率空间、Borel空间和正则测度的一个新的二分法定理(定理2.2)。粗略地说，如果M是测度空间中的紧凸集，则M中要么存在一个具有小局部基的点，要么存在一个具有大Maharam型的点。因此，我们的定理给出了拓扑学和测度论之间的联系。它也可以被视为纯粹的拓扑学或纯粹的测量理论陈述。本文的想法是受到文献[3]中推广定理4.3的尝试的启发，并成功地完成了(推论3.7)。作为我们的主要定理的推论，我们给出了一个定理的不同证明
A new dichotomy theorem for a space of probability, Radon measures is proved. Some applications of this result are given. In this paper we investigate some properties of measures on compact spaces. We prove a new dichotomy theorem for a space of probability, Borel and regular measures on a compact space (Theorem 2.2). Roughly speaking it says that if M is a compact, convex set in the space of measures then there either exists a point in M with a small local base, or there exists a point in M with a large Maharam type. Thus our theorem gives a connection between topology and measure theory. It can be also viewed as a purely topological or purely measure theoretical statement. The idea of this note was inspired by an attempt of generalizing Theorem 4.3 in [3], which was successfully done (Corollary 3.7). As a corollary to our main theorem, we give a dierent proof of a theorem due to