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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



A finitely additive generalization of the Fichtenholz-Lichtenstein theorem

Author: George Edward Sinclair
Journal: Trans. Amer. Math. Soc. 193 (1974), 359-374
MSC: Primary 28A35
MathSciNet review: 0417371
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Abstract: Let $ \mu $ and $ \nu $ be bounded, finitely additive measures on algebras over sets X and Y, respectively. Conditions are determined for a bounded function $ f:X \times Y \to {\mathbf{R}}$, without assuming bimeasurability, so that the iterated integrals $ \smallint_X {\smallint_Y {fd\mu d\mu } } $ and $ \smallint_Y {\smallint_X {fd\mu d\nu } } $ exist and are equal. This result is then used to construct a product algebra and finitely additive product measure for $ \mu $ and $ \nu $. Finally, a simple Fubini theorem with respect to this product algebra and product measure is established.

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Keywords: A-continuous, Dunford-Schwartz integral, finitely additive product measure, Fubini theorem, Pták lemma, Pták theorem, separately continuous, Stone-Čech compactification, Stone space
Article copyright: © Copyright 1974 American Mathematical Society

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