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The strong version of the Poincaré recurrence theorem states that for any probability space , any -measure preserving transformation and any almost every point of returns to 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].
Riečan, Beloslav. "A strengthening of the Poincaré recurrence theorem on MV-algebras." Applications of Mathematics 2012. Prague: Institute of Mathematics AS CR, 2012. 236-242. <http://eudml.org/doc/287843>.
@inProceedings{Riečan2012, abstract = {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 \rightarrow \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].}, author = {Riečan, Beloslav}, booktitle = {Applications of Mathematics 2012}, keywords = {Poincaré recurrence theorem; probability space; measure preserving transformation; MV-algebra}, location = {Prague}, pages = {236-242}, publisher = {Institute of Mathematics AS CR}, title = {A strengthening of the Poincaré recurrence theorem on MV-algebras}, url = {http://eudml.org/doc/287843}, year = {2012}, }
TY - CLSWK AU - Riečan, Beloslav TI - A strengthening of the Poincaré recurrence theorem on MV-algebras T2 - Applications of Mathematics 2012 PY - 2012 CY - Prague PB - Institute of Mathematics AS CR SP - 236 EP - 242 AB - 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 \rightarrow \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]. KW - Poincaré recurrence theorem; probability space; measure preserving transformation; MV-algebra UR - http://eudml.org/doc/287843 ER -