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Lusin's theorem for measure preserving homeomorphisms

Published online by Cambridge University Press:  26 February 2010

Steve Alpern  and
Robert D. Edwards
Steve Alpern
Affiliation:
University of California, Los Angeles, Los Angeles, CA.
Robert D. Edwards
Affiliation:
University of California, Los Angeles, Los Angeles, CA.
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Extract

We are concerned with invertible transformations of the unit n-dimensional cube In, 2 ≤ n ≤ ∞, which preserve n-dimensional Lebesgue measure μ. Following Halmos [4], we denote the space of all such transformations by G = G(In), and the subset of G consisting of homeomorphisms by M = M(In). We ask to what extent, and in what sense, can we approximate an arbitrary transformation g in G by a homeomorphism h in M. New results are obtained in the course of presenting a new proof of the theorem of J. Oxtoby and H. E. White, Jr., stated below.

Type
Research Article
Information
Mathematika , Volume 26 , Issue 1 , June 1979 , pp. 33 - 43
Copyright
Copyright © University College London 1979

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References

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