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Sibirsk. Mat. Zh., 2004, Volume 45, Number 1, Pages 80–102 (Mi smj1065)  

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

Order properties of the space of finitely additive transition functions

A. E. Gutmana, A. I. Sotnikovb

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
b Novosibirsk State University

Abstract: The basic order properties, as well as some metric and algebraic properties, are studied of the set of finitely additive transition functions on an arbitrary measurable space, as endowed with the structure of an ordered normed algebra, and some connections are revealed with the classical spaces of linear operators, vector measures, and measurable vector-valued functions. In particular, the question is examined of splitting the space of transition functions into the sum of the subspaces of countably additive and purely finitely additive transition functions.

Keywords: transition function, purely finitely additive measure, lifting of a measure space, vector measure, measurable vector-valued function, ordered vector space, vector lattice, Riesz space, $K$-space, Banach lattice, ordered Banach algebra

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English version:
Siberian Mathematical Journal, 2004, 45:1, 69–85

Bibliographic databases:

UDC: 517.98
Received: 15.10.2003

Citation: A. E. Gutman, A. I. Sotnikov, “Order properties of the space of finitely additive transition functions”, Sibirsk. Mat. Zh., 45:1 (2004), 80–102; Siberian Math. J., 45:1 (2004), 69–85

Citation in format AMSBIB
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\by A.~E.~Gutman, A.~I.~Sotnikov
\paper Order properties of the space of finitely additive transition functions
\jour Sibirsk. Mat. Zh.
\yr 2004
\vol 45
\issue 1
\pages 80--102
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\zmath{https://zbmath.org/?q=an:1053.46024}
\elib{https://elibrary.ru/item.asp?id=5215351}
\transl
\jour Siberian Math. J.
\yr 2004
\vol 45
\issue 1
\pages 69--85
\crossref{https://doi.org/10.1023/B:SIMJ.0000013013.03647.65}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000189126800006}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. I. Sotnikov, “Order properties of the space of strongly additive transition functions”, Siberian Math. J., 46:1 (2005), 166–171  mathnet  crossref  mathscinet  zmath  isi
  • Сибирский математический журнал Siberian Mathematical Journal
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