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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Products of two Borel measures


Author: Roy A. Johnson
Journal: Trans. Amer. Math. Soc. 269 (1982), 611-625
MSC: Primary 28C15; Secondary 03E35, 28A35
MathSciNet review: 637713
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Abstract: Let $ \mu $ and $ \nu $ be finite Borel measures on Hausdorff spaces $ X$ and $ Y$, respectively, and suppose product measures $ \mu \times {}_1\nu $ and $ \mu \times {}_2\nu $ are defined on the Borel sets of $ X \times Y$ by integrating vertical and horizontal cross-section measure, respectively. Sufficient conditions are given so that $ \mu \times {}_1\nu = \mu \times {}_2\nu $ and so that the usual product measure $ \mu \times \nu $ can be extended to a Borel measure on $ X \times Y$ by means of completion. Examples are given to illustrate these ideas.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1982-0637713-6
PII: S 0002-9947(1982)0637713-6
Keywords: Borel measure, purely atomic measure, separable-regular Borel measure, completion of a measure
Article copyright: © Copyright 1982 American Mathematical Society