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Issue:Central limit theorem on MV-algebras

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Title of paper: Central limit theorem on MV-algebras
Jana Kelemenová
Department of Mathematics, Faculty of Natural Sciences, Tajovskeho 40, 974 01 Banska Bystrica, Slovakia
Mária Kuková
Department of Mathematics, Faculty of Natural Sciences, Tajovskeho 40, 974 01 Banska Bystrica, Slovakia
Presented at: 11th IWGN, Sofia, 5 December 2010
Published in: Conference proceedings, pages 48—56
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Abstract: The aim is to approve the Central limit theorem on MV-algebras by the new approach, using the observable as a distribution function, and not the σ-homomorphism. The main idea is in local representation of σ-algebras. The following theorem is proved: Let M be a σ-complete MV-algebra with product, m : M 􀀀→ [0; 1] be a σ-additive state, (xn)n be a sequence of independent, equally distributed, square integrable observables. Hence E[x1] = E[x2] = ... = a; σ(x1) = σ(x2) = ... = σ. Then, for any t ∈ R


Keywords: MV-algebra, Central limit theorem
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