Construction of Regular Non-Atomic Strictly-Positive Measures in Second-Countable Non-Atomic Locally Compact Hausdorff Spaces

Autor:	Bentley, Jason
Rok vydání:	2018
Předmět:	Mathematics - Functional Analysis 28C15
Druh dokumentu:	Working Paper
Popis:	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. Comment: 11 to 12 pages total, 1 figure
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1807.05437 Zobrazit plný text záznamu View this record from Arxiv