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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
Abstract
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.
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- Copyright © Canadian Mathematical Society 1995