Additive set functions on lattices of sets

Author:
Gene A. DeBoth

Journal:
Trans. Amer. Math. Soc. **178** (1973), 341-355

MSC:
Primary 28A15; Secondary 60G45

DOI:
https://doi.org/10.1090/S0002-9947-1973-0333109-X

MathSciNet review:
0333109

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Abstract | References | Similar Articles | Additional Information

Abstract: This paper is concerned with properties of additive set functions defined on lattices of sets. Extensions of results of Brunk and Johansen, Darst, Johansen, and Uhl are obtained. Two fundamental approximation properties for lattices of sets (established in another paper) permit us to translate the setting and consider countably additive set functions defined on sigma lattices of sets. Thereby results for countably additive set functions defined on sigma lattices of sets are used to obtain alternate derivations and extensions of Darst's results for additive set functions defined on lattices of sets, i.e., we consider the Radon-Nikodym derivative, conditional expectation, and martingale convergence for lattices of sets.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1973-0333109-X

Keywords:
Lattice of sets,
algebra of sets,
finitely additive set functions,
sigma algebra,
sigma lattice,
-condition,
Orlicz space,
Radon-Nikodym derivative,
conditional expectation,
martingale

Article copyright:
© Copyright 1973
American Mathematical Society