Construction of regular non-atomic strictly-positive measures in second-countable non-atomic locally compact Hausdorff spaces

Jason Bentley

Published: 2022-03-22

Vol. 36 No. 1 (2022)

Construction of regular non-atomic strictly-positive measures in second-countable non-atomic locally compact Hausdorff spaces

Jason Bentley

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 set function limit that is extendable to a measure with the desired properties. Non-atomicity of the space provides a meticulous way to ensure that the set function limit is σ-additive.

Keywords:

regular measure , non-atomic measure , strictly-positive measure , locally compact spaces , non-atomic spaces , Polish spaces , regular spaces , second-countable spaces

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Bentley, J. (2022). Construction of regular non-atomic strictly-positive measures in second-countable non-atomic locally compact Hausdorff spaces. Annales Mathematicae Silesianae, 36(1), 15–25. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/13457

Construction of regular non-atomic strictly-positive measures in second-countable non-atomic locally compact Hausdorff spaces

Abstract

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