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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

An example concerning the Yosida-Hewitt decomposition of finitely additive measures


Author: Wolfgang Hensgen
Journal: Proc. Amer. Math. Soc. 121 (1994), 641-642
MSC: Primary 28A10; Secondary 28C15, 46E99
MathSciNet review: 1213861
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Abstract: Let $ \lambda $ be Lebesgue measure on the Lebesgue $ \sigma $-algebra $ \mathcal{L}$ of $ I:=]0,1[$. The author gives an example of a purely finitely additive measure $ \varphi :\mathcal{L} \to [0,1]$ vanishing on $ \lambda $-null sets such that $ \smallint f\,d\varphi = \smallint f\,d\lambda $ for every bounded continuous function f on I $ (f \in {C_b}(I))$. Consequently, $ \lambda - \varphi \in {L^\infty }(\lambda )'$ annihilates $ {C_b}(I)$ and is not purely finitely additive, contrary to an assertion of Yosida and Hewitt.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1213861-0
PII: S 0002-9939(1994)1213861-0
Keywords: Finitely additive measures, Yosida-Hewitt decomposition
Article copyright: © Copyright 1994 American Mathematical Society



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