Poincaré recurrence theorem in MV-algebras.
Beloslav Riečan · European Society for Fuzzy Logic and Technology Conference · 2009
The classical Poincare weak recurrence theorem states that for any probability space (Ω,S, P ), any P -measure preserving transformation T , and any A ∈ S, almost all points of A return to A. In the present paper the Poincare theorem is proved when the σ-algebra S is replaced by any σ-complete MV-algebra. Keywords— Measure preserving transformation, Poincare recurrence theorem, σ-complete MV-algebra.