Heaviness: An Extension of a Lemma of Y. Peres

Details Heaviness: An Extension of a Lemma of Y. Peres Heaviness: An Extension of a Lemma of Y. Peres

2009-06-22

arxiv.org/abs/0906.4001v1

Mathematics

Dynamical Systems

10 Pages, to appear in Houston Journal of Mathematics, one typo corrected

Scientific paper

We provide an elementary proof of Y. Peres' lemma on the existence in certain
dynamical systems of what we term heavy points, points whose ergodic averages
consistently dominate the expected value of the ergodic averages. We also
derive several generalizations of Peres' lemma by employing techniques from the
simplified proof.

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