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Strong Poincar

In: Mathematica Slovaca, vol. 60, no. 5
Beloslav Riečan
Detaily:
Rok, strany: 2010, 655 - 664
Kľúčové slová:
Poincaré recurrence theorem, probability space, measure preserving transformation, MV-algebra
O článku:
The classical Poincaré strong recurrence theorem states that for any probability space $(\Omega, \mathcal S, P)$, any $P$-measure preserving transformation $T$, and any $A \in \mathcal S$, almost all points of $A$ return to $A$ infinitely many times. In the present paper the Poincaré theorem is proved when the $\sigma$-algebra $\mathcal S$ is substituted by an MV-algebra of a special type. Another approach is used in [RIEČAN, B.: \textit{Poincaré recurrence theorem in MV-algebras}. In: Proc. IFSA-EUSFLAT 2009 (To appear)], where the weak variant of the theorem is proved, of course, for arbitrary MV-algebras. Such generalizations were already done in the literature, e.g. for quantum logic, see [DVUREČENSKIJ, A.: \textit{On some properties of transformations of a logic}, Math. Slovaca \textbf{26} (1976), 131--137.
Ako citovať:
ISO 690:
Riečan, B. 2010. Strong Poincar. In Mathematica Slovaca, vol. 60, no.5, pp. 655-664. 0139-9918. DOI: https://doi.org/10.2478/s12175-010-0038-2

APA:
Riečan, B. (2010). Strong Poincar. Mathematica Slovaca, 60(5), 655-664. 0139-9918. DOI: https://doi.org/10.2478/s12175-010-0038-2
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