# An Indicator Function Limit Theorem in Dynamical Systems

Abstract : We show by a constructive proof that in all aperiodic dynamical system, for all sequences $(a_n)_{n\in\N}\subset\R_+$ such that $a_n\nearrow\infty$ and $\frac{a_n}{n}\to 0$ as $n\to\infty$, there exists a set $A\in\A$ having the property that the sequence of the distributions of $(\frac{1}{a_{n}}S_{n}(\ind_A-\mu(A)))_{n\in\N}$ is dense in the space of all probability measures on $\R$.
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https://hal.archives-ouvertes.fr/hal-00331666
Contributor : Olivier Durieu <>
Submitted on : Friday, October 17, 2008 - 11:42:11 AM
Last modification on : Thursday, February 7, 2019 - 5:46:39 PM

### Citation

Olivier Durieu, Dalibor Volny. An Indicator Function Limit Theorem in Dynamical Systems. Stochastics and Dynamics, World Scientific Publishing, 2011, 11 (4), pp.681--690. ⟨10.1142/S0219493711003504⟩. ⟨hal-00331666⟩

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