Construction of regular non-atomic strictly-positive measures in second-countable non-atomic locally compact Hausdorff spaces
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
References
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Department of Mathematics, University of Central Florida, USA United States
https://orcid.org/0000-0002-0858-2178
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