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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: Download-icon.png PDF (153  Kb, 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
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  3. Mundici, D.: Interpretation of AFC*-algebras in Lukasiewicz sentential calculus. J. Funct. Anal 65, 1986, 15-63.
  4. Riečan B.: On the product MV-algebras. Tatra Mt. Math. Publ. 16, 1999, 143-149.
  5. Riečan, B., Lasova, L.: On the probability theory on the Kopka D-posets (to appear).
  6. Riečan, B., Mundici, D.: Probability on MV algebras, Handbook of Measue Theory, Elsevier, Amsterdam, 2002, 869-909.
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