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Hopf's Ergodic Theorem for Particles with Different Velocities and the "Strong Sweeping out Property"

Published online by Cambridge University Press:  20 November 2018

A. Bellow ,
A. P. Calderón  and
U. Krengel
A. Bellow
Affiliation:
Department of Mathematics, Northwestern University Evanston, Illinois 60208 U.S.A.
A. P. Calderón
Affiliation:
Department of Mathematics, University of Chicago Chicago, Illinois 60637 U.S.A.
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Abstract

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In an earlier paper we provided a counterexample to an old conjecture of Hopf. In this note we show that the "strong sweeping out property" obtains for the Hopf operators (Tt) both when t —> +∞ and when t —> 0+, that is a.e. convergence fails in the worst possible way.

Keywords

42B2560F15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 38 , Issue 1 , 01 March 1995 , pp. 11 - 15
Copyright
Copyright © Canadian Mathematical Society 1995

References

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