Measurability of functions in product spaces
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- by Kohur Gowrisankaran PDF
- Proc. Amer. Math. Soc. 31 (1972), 485-488 Request permission
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 $Y$.References
- Kohur Gowrisankaran, Iterated fine limits and iterated nontangential limits, Trans. Amer. Math. Soc. 173 (1972), 71–92. MR 311927, DOI 10.1090/S0002-9947-1972-0311927-0
- George W. Mackey, Induced representations of locally compact groups. I, Ann. of Math. (2) 55 (1952), 101–139. MR 44536, DOI 10.2307/1969423
- Mark Mahowald, On the measurability of functions in two variables, Proc. Amer. Math. Soc. 13 (1962), 410–411. MR 137812, DOI 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, Tata Institute of Fundamental Research Studies in Mathematics, No. 6, Published for the Tata Institute of Fundamental Research, Bombay by Oxford University Press, London, 1973. 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.
Additional Information
- © Copyright 1972 American Mathematical Society
- 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