Vol. 83, No. 2, 1979

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A Radon-Nikodým theorem for finitely additive bounded measures

Hugh Bardeen Maynard

Vol. 83 (1979), No. 2, 401–413

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
Received: 20 February 1979
Published: 1 August 1979
Hugh Bardeen Maynard