Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 
 

 

Bounded common extensions of charges


Authors: A. Basile, K. P. S. Bhaskara Rao and R. M. Shortt
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 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

Keywords: Finitely additive measure, bounded charge, common extension problem
Article copyright: © Copyright 1994 American Mathematical Society