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

R. B. Darst

Type: Article

Publication Date: 1970-12-01

Citations: 39

DOI: https://doi.org/10.2140/pjm.1970.35.581

Abstract

In the setting of additive set functions deίined on lattices of sets, a Lebesguβ decomposition and a Radon-Nikodym derivative are constructed and characterized.In the appropriate case (L 2 ), the Radon-Nikodym derivative is shown to be the conditional expectation.Finally, a martingale convergence theorem for Radon-Nikodym derivatives is obtained.

Locations

Pacific Journal of Mathematics - View - PDF
Project Euclid (Cornell University) - View - PDF

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