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Transactions of the American Mathematical Society

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On Borel mappings and Baire functions


Author: R. W. Hansell
Journal: Trans. Amer. Math. Soc. 194 (1974), 195-211
MSC: Primary 54H05; Secondary 54C50
MathSciNet review: 0362270
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Abstract: This paper studies conditions under which classes of Borel mappings (i.e., mappings such that the inverse image of open sets are Borel sets) coincide with certain classes of Baire functions (i.e., functions which belong to the smallest family containing the continuous functions and closed with respect to pointwise limits). Generalizations of the classical Lebesgue-Hausdorff and Banach theorems are obtained for the class of mappings which we call ``$ \sigma $-discrete". These results are then applied to the problem of extending Borel mappings over Borel sets, and generalizations of the theorems of Lavrentiev and Kuratowski are obtained.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1974-0362270-7
Keywords: Borel measurable mappings, Baire functions, Borel classifications, Baire classifications, $ \sigma $-discrete mappings
Article copyright: © Copyright 1974 American Mathematical Society