Notes on product measures for Math 501 , Fall 2010
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چکیده
for any finite disjoint union ∪j=1Aj ×Bj of rectangles. It is easy to see, by considering a common refinement of any two representations of a set in A as a finite disjoint union of rectangles that m does not depend on the representation, and is well-defined premeasure on A. 1.2 DEFINITION (Product sigma-algebra). For any two measure spaces (X,M, μ) and (Y,N , μ), the product sigma algebra in X × Y , denoted by M⊗N , is the smallest sigma algebra containing the rectangle algebra A. 1 c © 2010 by the author. This article may be reproduced, in its entirety, for non-commercial purposes.
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