Vol. 72, No. 2, 1977

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A decomposition of additive set functions

Wayne C. Bell

Vol. 72 (1977), No. 2, 305–311
Abstract

In this paper it is demonstrated that if μ is an additive function from a field F into the nonnegative reals, then μ can be separated into two mutually singular parts, μ1 and μ2, where μ1 is representable in the sense that its Lebesgue decomposition projection operator has a refinement integral representation and μ2 is such that for each E F the contraction of μ2 to E is representable iff μ2(E) = 0. If μ2 is maximal, then the decomposition is unique.

Mathematical Subject Classification 2000
Primary: 28A10
Milestones
Received: 29 October 1976
Revised: 25 April 1977
Published: 1 October 1977
Authors
Wayne C. Bell