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On sums of indicator functions in dynamical systems

Published online by Cambridge University Press:  13 October 2009

OLIVIER DURIEU  and
DALIBOR VOLNÝ
OLIVIER DURIEU
Affiliation:
Laboratoire de Mathématiques Raphaël Salem, UMR 6085 CNRS-Université de Rouen, France (email: [email protected], [email protected])
DALIBOR VOLNÝ
Affiliation:
Laboratoire de Mathématiques Raphaël Salem, UMR 6085 CNRS-Université de Rouen, France (email: [email protected], [email protected])
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Abstract

In this paper, we are interested in the limit theorem question for sums of indicator functions. We show that in every invertible ergodic dynamical system, for every increasing sequence (an)n∈ℕ⊂ℝ+ such that an↗∞ and an/n→0 as n→∞, there exists a dense Gδ of measurable sets A such that the sequence of the distributions of the partial sums is dense in the set of the probability measures on ℝ.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 30 , Issue 5 , October 2010 , pp. 1419 - 1430
Copyright
Copyright © Cambridge University Press 2009

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