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Issue:Central limit theorem on MV-algebras

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http://ifigenia.org/wiki/issue:iwgn-2010-48-56
Title of paper: Central limit theorem on MV-algebras
Author(s):
Jana Kelemenová
Department of Mathematics, Faculty of Natural Sciences, Tajovskeho 40, 974 01 Banska Bystrica, Slovakia
kelemen@fpv.umb.sk
Mária Kuková
Department of Mathematics, Faculty of Natural Sciences, Tajovskeho 40, 974 01 Banska Bystrica, Slovakia
kukova@fpv.umb.sk
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

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Keywords: MV-algebra, Central limit theorem
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  4. Riečan B.: On the product MV-algebras. Tatra Mt. Math. Publ. 16, 1999, 143-149.
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  6. Riečan, B., Mundici, D.: Probability on MV algebras, Handbook of Measue Theory, Elsevier, Amsterdam, 2002, 869-909.
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