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Diskr. Mat., 2008, Volume 20, Issue 3, Pages 19–27 (Mi dm1009)  

This article is cited in 1 scientific paper (total in 1 paper)

Finite probabilistic structures

V. M. Maksimov


Abstract: Consideration of the field of events in the theory of probability gives rise to the notion of the field of events $\mathscr F(B)$ consisting of a set of subsets of some set $B$. On the field $\mathscr F(B)$, two algebraic structures are naturally defined. These are the Boolean algebra $\mathscr A(\mathscr F(B))$ with the operations of union, intersection and complement, and the lattice $L(\mathscr F(B))$, where the order is defined according to inclusion of the sets of $\mathscr F(B)$. In this paper, we consider one more algebraic structure on $\mathscr F(B)$ and the abstract variant of this structure, the so-called probabilistic structure, which is closely related to properties of the measure on $\mathscr F(B)$.

DOI: https://doi.org/10.4213/dm1009

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English version:
Discrete Mathematics and Applications, 2008, 18:4, 341–350

Bibliographic databases:

UDC: 519.2
Received: 15.05.2007
Revised: 20.06.2008

Citation: V. M. Maksimov, “Finite probabilistic structures”, Diskr. Mat., 20:3 (2008), 19–27; Discrete Math. Appl., 18:4 (2008), 341–350

Citation in format AMSBIB
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\by V.~M.~Maksimov
\paper Finite probabilistic structures
\jour Diskr. Mat.
\yr 2008
\vol 20
\issue 3
\pages 19--27
\mathnet{http://mi.mathnet.ru/dm1009}
\crossref{https://doi.org/10.4213/dm1009}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2467450}
\elib{http://elibrary.ru/item.asp?id=20730249}
\transl
\jour Discrete Math. Appl.
\yr 2008
\vol 18
\issue 4
\pages 341--350
\crossref{https://doi.org/10.1515/DMA.2008.024}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-53349154214}


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  • https://doi.org/10.4213/dm1009
  • http://mi.mathnet.ru/eng/dm/v20/i3/p19

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. M. Maximov, “Multidimensional and abstract probability”, Proc. Steklov Inst. Math., 287:1 (2014), 174–201  mathnet  crossref  crossref  isi  elib  elib
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