Vol. 46, No. 1, 1973

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Uniform integrability of derivatives on σ-lattices

Allan Francis Abrahamse

Vol. 46 (1973), No. 1, 1–10
Abstract

This paper contains a new derivation of the Radon-Nikodym derivative on a σ-lattice. Absolute continuity is defined in this setting, and the definition is justified by obtaining an extension of a standard result on the uniform integrability of derivatives. An application to mean convergence of martingales and a version of Jensen’s inequality are given.

Mathematical Subject Classification 2000
Primary: 28A15
Secondary: 60A10
Milestones
Received: 10 January 1972
Revised: 27 April 1972
Published: 1 May 1973
Authors
Allan Francis Abrahamse