Finitely additive measures

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On finitely additive vector measures.

In this paper we extend the well-known Vitali-Hahn-Saks and Nikodým theorems for measures to finitely additive vector-valued set functions.

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Let L be a linear space of real bounded random variables on the probability space (Ω,A, P0). There is a finitely additive probability P on A, such that P ∼ P0 and EP (X) = 0 for all X ∈ L, if and only if c EQ(X) ≤ ess sup(−X), X ∈ L, for some constant c > 0 and (countably additive) probability Q on A such that Q ∼ P0. A necessary condition for such a P to exist is L − L+∞ ∩ L + ∞ = {0}, where t...

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An Isomorphism Theorem for Finitely Additive Measures

A problem which is appealing to the intuition in view of the relative frequency interpretation of probability is to define a measure on a countable space which assigns to each point the measure 0. Such a measure of course becomes trivial if it is countably additive. Finitely additive measures of this type have been discussed by R. C. Buck [l] and by E. F. Buck and R. C. Buck [2]. In a discussio...

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Finitely additive measures on groups and rings

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ژورنال

عنوان ژورنال: Transactions of the American Mathematical Society

سال: 1952

ISSN: 0002-9947

DOI: 10.1090/s0002-9947-1952-0045194-x