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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The Mackey continuity of the monotone rearrangement
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by Anthony Horsley and Andrzej J. Wrobel PDF
Proc. Amer. Math. Soc. 97 (1986), 626-628 Request permission

Abstract:

Let $(A, \mathcal {A},\mu )$ be a probability space, and let mes denote the Lebesgue measure on the Borel $\sigma$-algebra $\mathcal {B}$ in $[0,1]$. The nondecreasing-rearrangement operator from the space ${L^\infty }(\mu ) = {L^\infty }(A, \mathcal {A}, \mu )$ of real-valued essentially bounded functions into ${L^\infty } = {L^\infty }([0,1]$, $\mathcal {B}$, mes) is shown to be uniformly continuous in the Mackey topologies $\tau ({L^\infty }(\mu )$, ${L^1}(\mu ))$ and $\tau ({L^\infty },{L^1})$ on ${L^\infty }(\mu )$ and ${L^\infty }$, respectively.
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Additional Information
  • © Copyright 1986 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 97 (1986), 626-628
  • MSC: Primary 46E30
  • DOI: https://doi.org/10.1090/S0002-9939-1986-0845977-8
  • MathSciNet review: 845977