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La semicontinuité et la propriété de Baire


Authors: Z. Grande and S. Stawikowska
Journal: Proc. Amer. Math. Soc. 77 (1979), 48-52
MSC: Primary 26A15
DOI: https://doi.org/10.1090/S0002-9939-1979-0539629-8
MathSciNet review: 539629
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Abstract: Let X, Y be two metric separable and complete spaces and R be a set of all reals numbers. If all sections $ {f_x}(y) = f(x,y)\;(x \in X$ and $ y \in Y)$ of a function $ f:X \times Y \to R$ are almost qualitative upper semiequicontinuous and upper semicontinuous [upper semiequicontinuous] and if all sections $ {f^y}(x) = f(x,y)$ have the Baire property [are borelien], then the function f has the Baire property [is borelien].


References [Enhancements On Off] (What's this?)

  • [1] Z. Grande, La propriété de Baire des fonctions de deux variables ponctuelement discontinues par rapport à une variable, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 25 (1977), 535-539.
  • [2] J. Oxtoby, La mesure et la catégorie, Moscou, 1974. (Russe)

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DOI: https://doi.org/10.1090/S0002-9939-1979-0539629-8
Article copyright: © Copyright 1979 American Mathematical Society