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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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On Borel mappings and Baire functions
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by R. W. Hansell PDF
Trans. Amer. Math. Soc. 194 (1974), 195-211 Request permission

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
  • © Copyright 1974 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 194 (1974), 195-211
  • MSC: Primary 54H05; Secondary 54C50
  • DOI: https://doi.org/10.1090/S0002-9947-1974-0362270-7
  • MathSciNet review: 0362270