Issue:Strong law of large numbers on MV-algebras

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http://ifigenia.org/wiki/issue:iwgn-2010-75-82

Title of paper: Strong law of large numbers on MV-algebras Author(s): Mária Kuková Department of Mathematics, Faculty of Natural Sciences, Tajovskeho 40, 974 01 Banska Bystrica, Slovakia kukova@fpv.umb.sk Jana Kelemenová Department of Mathematics, Faculty of Natural Sciences, Tajovskeho 40, 974 01 Banska Bystrica, Slovakia kelemen@fpv.umb.sk Presented at: 11th IWGN, Sofia, 5 December 2010 Published in: Conference proceedings, pages 75—82 Download:  PDF (153  Kb, File info) Abstract: The aim is to approve the Strong law of large numbers on MV-algebras by the new approach, using the observable as a distribution function, and not a σ-homomorphism. The main idea is in a 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 square integrable observables, such that Σn=1∞ σ2(xn) / n2 < ∞. Then limp→∞limk→∞limi→∞(∧n=kk+i(1/n Σj=1n(xj − E(xj)) (− 1/p, 1/p)) = 1 Keywords: MV-algebra, Central limit theorem References: Kopka, F.: D-posets with meet function. Advances in Electrical Engineering 3, 2004, 34-36. Montagna, F.: An algebraic approach to propositional fuzzy logic. J. Logic Lang. Inf. 2000, 91-124. Mundici, D.: Interpretation of AFC*-algebras in Lukasiewicz sentential calculus. J. Funct. Anal 65, 1986, 15-63. Riečan B.: On the product MV-algebras. Tatra Mt. Math. Publ. 16, 1999, 143-149. Riečan, B., Lasova, L.: On the probability theory on the Kopka D-posets (to appear). Riečan, B., Mundici, D.: Probability on MV algebras, Handbook of Measue Theory, Elsevier, Amsterdam, 2002, 869-909. Citations: The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page.