Translator Disclaimer
2022 Comments on Charges on the Boolean Algebra of Regular Open Sets
K. P. S. Bhaskara Rao
Author Affiliations +
Real Anal. Exchange 47(1): 97-102 (2022). DOI: 10.14321/realanalexch.47.1.1600145293

Abstract

This paper has three main results. The first result is an extension theorem for charges on the Boolean algebra of regular open sets of a topological space. The second result is an abstract form of the first result, which we call an abstract extension theorem for charges on Boolean algebras. The third result is a characterization of regular open sets in $R$. The first two results are useful for integration of functions on topological spaces with respect to charges on Boolean algebras of regular open sets. The third result is useful in proving that the Lebesgue measure is not a charge when restricted to the Boolean algebra of regular open sets (see [3])

Citation

Download Citation

K. P. S. Bhaskara Rao. "Comments on Charges on the Boolean Algebra of Regular Open Sets." Real Anal. Exchange 47 (1) 97 - 102, 2022. https://doi.org/10.14321/realanalexch.47.1.1600145293

Information

Published: 2022
First available in Project Euclid: 13 June 2022

Digital Object Identifier: 10.14321/realanalexch.47.1.1600145293

Subjects:
Primary: 28A10
Secondary: 03E99 , 06E05 , 28A05

Keywords: Boolean algebra of regular open sets , charges , extension theorem , regular open set

Rights: Copyright © 2022 Michigan State University Press

JOURNAL ARTICLE
6 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.47 • No. 1 • 2022
Back to Top