Short Communications: Convergence of Integrals of UnboundedReal Functions in Random Measures

$\sm$-additive random measures and integrals with respect to them of real valued functions are considered in the most general setting. The statement of convergence of $\int f\,d\mu_n\tlp\int f\,d\mu$, $\ny$, is proved under conditions similar to uniform integrability. An analogue of the Valle--Pouss...

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Bibliographic Details
Published in:Theory of probability and its applications 1998-04, Vol.42 (2), p.310-314
Main Author: Radchenko, V. N.
Format: Article
Language:English
Subjects:
Algebra
Inequality
Integrals
Random variables
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Summary:$\sm$-additive random measures and integrals with respect to them of real valued functions are considered in the most general setting. The statement of convergence of $\int f\,d\mu_n\tlp\int f\,d\mu$, $\ny$, is proved under conditions similar to uniform integrability. An analogue of the Valle--Poussin theorem is established. A criterion is given for the relation $\int f_ng d\mu\tlp\int g\,d\eta$, $\ny$, to hold for all bounded g.
ISSN:0040-585X
1095-7219
DOI:10.1137/S0040585X97976179