Uniform integrability of derivatives on σ-lattices

Allan Francis Abrahamse

Vol. 46 (1973), No. 1, 1–10

DOI: 10.2140/pjm.1973.46.1

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