Abstract
The classical Poincaré strong recurrence theorem states that for any probability space (Ω, ℒ, P), any P-measure preserving transformation T, and any A ∈ ℒ, almost all points of A return to A infinitely many times. In the present paper the Poincaré theorem is proved when the σ-algebra ℒ is substituted by an MV-algebra of a special type. Another approach is used in [RIEČAN, B.: 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.: On some properties of transformations of a logic, Math. Slovaca 26 (1976), 131–137.
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Communicated by Anatolij Dvurečenskij
Dedicated to Professor Sylvia Pulmannová on the occasion of her 70th birthday
The paper was supported by grant VEGA 1/2002/05 and grant APVV LPP-0046-06.
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Riečan, B. Strong Poincaré recurrence theorem in MV-algebras. Math. Slovaca 60, 655–664 (2010). https://doi.org/10.2478/s12175-010-0038-2
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DOI: https://doi.org/10.2478/s12175-010-0038-2