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Article

Riečan, Beloslav
A strengthening of the Poincaré recurrence theorem on MV-algebras. (English). In: Brandts, J., Chleboun, J., Korotov, S., Segeth, K., Šístek, J. and Vejchodský, T. (eds.): Applications of Mathematics 2012, In honor of the 60th birthday of Michal Křížek. Proceedings. Prague, May 2-5, 2012. Institute of Mathematics AS CR, Prague, 2012. pp. 236-242
MSC: 06D35, 28D05, 60A10, 60E10 | MR 3204415 | Zbl 1313.60001
Keywords:
Poincaré recurrence theorem; probability space; measure preserving transformation; MV-algebra
Summary:
The strong version of the Poincaré recurrence theorem states that for any probability space $(\Omega, \mathcal S, P)$, any $P$-measure preserving transformation $T:\Omega \to \Omega$ and any $A \in \mathcal S$ almost every point of $A$ returns to $A$ infinitely many times. In [8] (see also [4]) the theorem has been proved for MV-algebras of some type. The present paper contains a remarkable strengthening of the result stated in [8].
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