A decomposition of additive set functions

Wayne C. Bell

Vol. 72 (1977), No. 2, 305–311

DOI: 10.2140/pjm.1977.72.305

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