## Additive set functions on lattices of sets

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- by Gene A. DeBoth PDF
- Trans. Amer. Math. Soc.
**178**(1973), 341-355 Request permission

## 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.## References

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*Norm convergence of martingales of Radón-Nikodym derivatives given a*$\sigma$-

*lattice*, Pacific J. Math. (to appear). —,

*Two approximation properties and a Radón Nikodym derivative for lattices of sets*(to appear).

## Additional Information

- © Copyright 1973 American Mathematical Society
- 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