<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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 <italic>σ</italic>-additive.</p>
</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.

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

Annales Mathematicae Silesianae

This work is licensed under the Creative Commons Attribution 4.0 International License.

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...

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

Published Online: Mar 22, 2022

Page range: 15 - 25

Received: Jun 17, 2021

Accepted: Mar 06, 2022

DOI: https://doi.org/10.2478/amsil-2022-0005

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

© 2022 Jason Bentley, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

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

Published Online: Mar 22, 2022

Page range: 15 - 25

Received: Jun 17, 2021

Accepted: Mar 06, 2022

DOI: https://doi.org/10.2478/amsil-2022-0005

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

© 2022 Jason Bentley, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

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