La semicontinuité et la propriété de Baire
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- by Z. Grande and S. Stawikowska PDF
- Proc. Amer. Math. Soc. 77 (1979), 48-52 Request permission
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
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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.
J. Oxtoby, La mesure et la catégorie, Moscou, 1974. (Russe)
Additional Information
- © Copyright 1979 American Mathematical Society
- 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