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Journal: Annales Mathematicae Silesianae

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

Jason Bentley

Language: EN | Published: 22-03-2022 | Abstract | pp. 15-25

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.

2022-03-22