Construction of Regular Non-Atomic Strictly-Positive Measures in Second-Countable Non-Atomic Locally Compact Hausdorff Spaces
Functional Analysis
2020-02-21 v3
Abstract
This paper presents a constructive proof of the existence of a regular non-atomic strictly-positive measure on any second-countable non-atomic locally compact Hausdorff space. This construction involves a sequence of finitely-additive set functions defined recursively on an ascending sequence of rings of subsets with a premeasure limit that is extendable to a measure with the desired properties. Non-atomicity of the space provides a non-trivial way to ensure that the limit is a premeasure.
Keywords
Cite
@article{arxiv.1807.05437,
title = {Construction of Regular Non-Atomic Strictly-Positive Measures in Second-Countable Non-Atomic Locally Compact Hausdorff Spaces},
author = {Jason Bentley},
journal= {arXiv preprint arXiv:1807.05437},
year = {2020}
}
Comments
11 to 12 pages total, 1 figure