On the associativity of the product of measure spaces

Author: Horváth, L.

Source: Acta Mathematica Hungarica, Volume 98, Number 4, 2003 , pp. 301-310(10)

Publisher: Springer

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Abstract:



If we arbitrarily choose finitely many measure spaces, then the existence of a product of these measure spaces can be proved. It is well known that this operation is not associative which is a substantial difficulty. In this paper we show that the associative law remains true between the -algebras of the product spaces, and we give an extension of the Fubini's theorem.

Keywords: Fubini's theorem; product measure

Document Type: Research Article

Affiliations: Department of Mathematics and Computing, University of Veszprém 8200, Veszprém, Egyetem u. 10, Hungary E-mail: LHORVATH@ALMOS.VEIN.HU

Publication date: January 1, 2003

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