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On some property of functions defined on $ \mathbf{R}^2$ that are $ \mathcal{I}$-approximately continuous with respect to one variable


Authors: R. Carrese and E. Łazarow
Journal: Proc. Amer. Math. Soc. 116 (1992), 377-380
MSC: Primary 26A21
DOI: https://doi.org/10.1090/S0002-9939-1992-1097337-8
MathSciNet review: 1097337
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Abstract: Balcerzak, Lazarow, and Wilczyński proved that every separately $ \mathcal{I}$-approximately continuous function is Baire 2. In this paper we shall prove that if $ f$ is a function $ \mathcal{I}$-approximately continuous with respect to one of its variables and of the $ \alpha $-class of Baire with respect to the other one, then $ f$ is of the $ (\alpha + 1)$-class of Baire in $ {R^2}$.


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DOI: https://doi.org/10.1090/S0002-9939-1992-1097337-8
Article copyright: © Copyright 1992 American Mathematical Society