The Mackey continuity of the monotone rearrangement

Authors:
Anthony Horsley and Andrzej J. Wrobel

Journal:
Proc. Amer. Math. Soc. **97** (1986), 626-628

MSC:
Primary 46E30

MathSciNet review:
845977

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Abstract: Let be a probability space, and let mes denote the Lebesgue measure on the Borel -algebra in . The nondecreasing-rearrangement operator from the space of real-valued essentially bounded functions into , , mes) is shown to be uniformly continuous in the Mackey topologies , and on and , respectively.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1986-0845977-8

Keywords:
Nondecreasing rearrangement,
Mackey topology

Article copyright:
© Copyright 1986
American Mathematical Society