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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Convergence in measure for semigroup-valued integrals


Author: Isidore Fleischer
Journal: Proc. Amer. Math. Soc. 101 (1987), 299-305
MSC: Primary 28B10; Secondary 46G10
MathSciNet review: 902545
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Abstract: The semigroup-valued integral of M. Sion [S] is reformulated for a general notion of approximation by sums of values taken by a set function integrand. A convergence in measure theorem is established, which yields both his pointwise dominated convergence theorem as well as an integrability criterion which specializes to his existence theorem.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0902545-8
PII: S 0002-9939(1987)0902545-8
Article copyright: © Copyright 1987 American Mathematical Society