Measurability of functions in product spaces
Author:
Kohur Gowrisankaran
Journal:
Proc. Amer. Math. Soc. 31 (1972), 485-488
MSC:
Primary 28A35
DOI:
https://doi.org/10.1090/S0002-9939-1972-0291403-X
MathSciNet review:
0291403
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Abstract | References | Similar Articles | Additional Information
Abstract: Let $f$ be a function on a product space $X \times Y$ with values in a separable metrizable space such that it is measurable in one variable and continuous in the other. The joint measurability of such a function is proved under certain conditions on $X$ and $Y$.
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- George W. Mackey, Induced representations of locally compact groups. I, Ann. of Math. (2) 55 (1952), 101–139. MR 44536, DOI https://doi.org/10.2307/1969423
- Mark Mahowald, On the measurability of functions in two variables, Proc. Amer. Math. Soc. 13 (1962), 410–411. MR 137812, DOI https://doi.org/10.1090/S0002-9939-1962-0137812-4
- Walter Rudin, Real and complex analysis, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0210528
- Laurent Schwartz, Radon measures on arbitrary topological spaces and cylindrical measures, Published for the Tata Institute of Fundamental Research, Bombay by Oxford University Press, London, 1973. Tata Institute of Fundamental Research Studies in Mathematics, No. 6. MR 0426084 W. Sierpiński, Sur un probleme concernant les ensembles measurables superficiellment, Fund. Math. 1 (1920), 112-115. H. D. Ursell, Some methods of proving measurability, Fund. Math. 32 (1939), 311-330.
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Additional Information
Keywords:
Measurability,
product spaces,
Radon measures,
Suslin space,
Polish space
Article copyright:
© Copyright 1972
American Mathematical Society
