On topological spaces possessing uniformly distributed sequences
V.I. Bogachev, M.N. Lukintsova
TL;DR
This paper introduces two classes of topological spaces where probability Radon measures have uniformly distributed sequences, and shows these classes are stable under certain product operations.
Contribution
It defines new classes of topological spaces with uniformly distributed sequences and proves their stability under multiplication by Souslin spaces.
Findings
Every probability Radon measure on these spaces has a uniformly distributed sequence.
The classes are stable under multiplication by completely regular Souslin spaces.
Provides conditions ensuring the existence of uniformly distributed sequences in these spaces.
Abstract
Two classes of topological spaces are introduced on which every probability Radon measure possesses a uniformly distributed sequence or a uniformly tight uniformly distributed sequence. It is shown that these classes are stable under multiplication by completely regular Souslin spaces
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Taxonomy
TopicsAdvanced Topology and Set Theory · Computability, Logic, AI Algorithms · Fuzzy and Soft Set Theory