Vol. 35, No. 3, 1970

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The Lebesgue decomposition, Radon-Nikodym derivative, conditional expectation, and martingale convergence for lattices of sets

Richard Brian Darst

Vol. 35 (1970), No. 3, 581–600
Abstract

In the setting of additive set functions defined on lattices of sets, a Lebesgue decomposition and a Radon-Nikodym derivative are constructed and characlerized. In the appropriate case (L2), the Radon-Nikodym derivative is shown to be the conditional expectation. Finally, a martingale convergence theorem for Radon-Nikodym derivatives is obtained.

Mathematical Subject Classification 2000
Primary: 28A10
Secondary: 60B99
Milestones
Received: 24 July 1969
Revised: 10 April 1970
Published: 1 December 1970
Authors
Richard Brian Darst