An example concerning the Yosida-Hewitt decomposition of finitely additive measures
Proc. Amer. Math. Soc. 121 (1994), 641-642
Primary 28A10; Secondary 28C15, 46E99
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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.
Hensgen, Some properties of the vector-valued Banach ideal space
𝐸(𝑋) derived from those of 𝐸 and 𝑋,
Collect. Math. 43 (1992), no. 1, 1–13. MR 1214219
Yosida and Edwin
Hewitt, Finitely additive measures,
Trans. Amer. Math. Soc. 72 (1952), 46–66. MR 0045194
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.
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