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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: olivier.durieu@univ-rouen.fr, dalibor.volny@univ-rouen.fr)
DALIBOR VOLNÝ
Affiliation:
Laboratoire de Mathématiques Raphaël Salem, UMR 6085 CNRS-Université de Rouen, France (email: olivier.durieu@univ-rouen.fr, dalibor.volny@univ-rouen.fr)
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Abstract

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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 $(\sfrac {1}{a_n})\sum _{i=0}^{n-1}(\ind _A-\mu (A))\circ T^i$ is dense in the set of the probability measures on ℝ.

Information

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

References

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