Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Bounded common extensions of charges
HTML articles powered by AMS MathViewer

by A. Basile, K. P. S. Bhaskara Rao and R. M. Shortt PDF
Proc. Amer. Math. Soc. 121 (1994), 137-143 Request permission

Abstract:

Let $\mathcal {A}$ and $\mathcal {B}$ be fields of subsets of a set X and let $\mu :\mathcal {A} \to {\mathbf {R}}$ and $\nu :\mathcal {B} \to {\mathbf {R}}$ be consistent, bounded, finitely additive measures (i.e., charges). We give necessary and sufficient conditions for $\mu$ and $\nu$ to have a bounded common extension to $\mathcal {A} \vee \mathcal {B}$. Conditions on $\mathcal {A}$ and $\mathcal {B}$ are given under which any bounded consistent charges $\mu$ and $\nu$ have a bounded common extension.
References
  • K. P. S. Bhaskara Rao and M. Bhaskara Rao, Theory of charges, Pure and Applied Mathematics, vol. 109, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York, 1983. A study of finitely additive measures; With a foreword by D. M. Stone. MR 751777
  • Zbigniew Lipecki, On common extensions of two quasimeasures, Czechoslovak Math. J. 36(111) (1986), no. 3, 489–494. MR 847776
  • Klaus D. Schmidt and Gerd Waldschaks, Common extensions of order bounded vector measures, Rend. Circ. Mat. Palermo (2) Suppl. 28 (1992), 117–124. Measure theory (Oberwolfach, 1990). MR 1183045
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 28A12
  • Retrieve articles in all journals with MSC: 28A12
Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 121 (1994), 137-143
  • MSC: Primary 28A12
  • DOI: https://doi.org/10.1090/S0002-9939-1994-1176064-4
  • MathSciNet review: 1176064