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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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Extreme limits of compacta valued functions
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by T. F. Bridgland PDF
Trans. Amer. Math. Soc. 170 (1972), 149-163 Request permission

Abstract:

Let $X$ denote a topological space and $\Omega (X)$ the space of all nonvoid closed subsets of $X$. Recent developments in analysis, especially in control theory, have rested upon the properties of the space $\Omega (X)$ where $X$ is assumed to be metric but not necessarily compact and with $\Omega (X)$ topologized by the Hausdorff metric. For a continuation of these developments, it is essential that definitions of extreme limits of sequences in $\Omega (X)$ be formulated in such a way that the induced limit is topologized by the Hausdorff metric. It is the purpose of this paper to present the formulation of such a definition and to examine some of the ramifications thereof. In particular, we give several theorems which embody “estimates of Fatou” for integrals of set valued functions.
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 170 (1972), 149-163
  • MSC: Primary 54C60; Secondary 28A45
  • DOI: https://doi.org/10.1090/S0002-9947-1972-0362209-2
  • MathSciNet review: 0362209