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 be Lebesgue measure on the Lebesgue -algebra of . The author gives an example of a purely finitely additive measure vanishing on -null sets such that for every bounded continuous function f on I . Consequently, annihilates and is not purely finitely additive, contrary to an assertion of Yosida and Hewitt.
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- [HY] Kôsaku Yosida and Edwin Hewitt, Finitely additive measures, Trans. Amer. Math. Soc. 72 (1952), 46–66. MR 0045194, https://doi.org/10.1090/S0002-9947-1952-0045194-X
- [IT] A. and C. Ionescu-Tulcea, Topics in the theory of lifting, Ergeb. Math. Grenzgeb. (3), vol. 48, Springer, Berlin, 1969.
- W. Hensgen, Contributions to the geometry of vector-valued and spaces, Habilitation Thesis, Regensburg, 1992. MR 1214219 (95a:46058)
- E. Hewitt and K. Yosida, Finitely additive measures, Trans. Amer. Math. Soc. 72 (1952), 46-66. MR 0045194 (13:543b)
- A. and C. Ionescu-Tulcea, Topics in the theory of lifting, Ergeb. Math. Grenzgeb. (3), vol. 48, Springer, Berlin, 1969.
Keywords: Finitely additive measures, Yosida-Hewitt decomposition
Article copyright: © Copyright 1994 American Mathematical Society