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)

 

 

The Hahn decomposition theorem


Author: Raouf Doss
Journal: Proc. Amer. Math. Soc. 80 (1980), 377
MSC: Primary 28A12
MathSciNet review: 577778
Full-text PDF Free Access

Abstract | Similar Articles | Additional Information

Abstract: Let $ (X,\mathcal{A},\mu )$ be a signed measure on the $ \sigma $-algebra $ \mathcal{A}$ of subsets of X. We give a very short proof of the Hahn decomposition theorem, namely, that X can be partitioned into two subsets P and N such that P is positive: $ \mu (E) \geqslant 0$ for every $ E \subset P$, and N is negative: $ \mu (E) \leqslant 0$ for every $ E \subset N$.


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 28A12

Retrieve articles in all journals with MSC: 28A12


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0577778-7
Article copyright: © Copyright 1980 American Mathematical Society