A Radon-Nikodým theorem for finitely additive bounded measures

Hugh Bardeen Maynard

Vol. 83 (1979), No. 2, 401–413

DOI: 10.2140/pjm.1979.83.401

Abstract

An exact Radon-Nikodym theorem is obtained for finitely additive bounded scalar measures defined on a field, the additional condition being a local condition on the dominant average range. The traditional technique of transferring the problem to the Stone space, which results in approximate Radon-Nikodym derivatives, is circumvented by isolating an Exhaustion principal for finitely additive measures which is then utilized to obtain the necessary decompositions.

Mathematical Subject Classification 2000

Primary: 28A15

Secondary: 28A25

Milestones

Received: 20 February 1979

Published: 1 August 1979