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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality 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 1.43.

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Convergence of functions: equi-semicontinuity
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by Szymon Dolecki, Gabriella Salinetti and Roger J.-B. Wets PDF
Trans. Amer. Math. Soc. 276 (1983), 409-430 Request permission

Abstract:

We study the relationship between various types of convergence for extended real-valued functionals engendered by the associated convergence of their epigraphs; pointwise convergence being treated as a special case. A condition of equi-semicontinuity is introduced and shown to be necessary and sufficient to allow the passage from one type of convergence to another. A number of compactness criteria are obtained for families of semicontinuous functions; in the process we give a new derivation of the Arzelá-Ascoli Theorem.
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Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 276 (1983), 409-430
  • MSC: Primary 58E30; Secondary 49D99, 54A20
  • DOI: https://doi.org/10.1090/S0002-9947-1983-0684518-7
  • MathSciNet review: 684518