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Sibirskii Matematicheskii Zhurnal, 2004, Volume 45, Number 1, Pages 80–102 (Mi smj1065)  
This article is cited in 3 scientific papers (total in 3 papers)

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
Full-text PDF (341 kB) Citations (3)
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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.
Received: 15.10.2003
English version:
Siberian Mathematical Journal, 2004, Volume 45, Issue 1, Pages 69–85
DOI: https://doi.org/10.1023/B:SIMJ.0000013013.03647.65
Bibliographic databases:
UDC: 517.98
Language: Russian
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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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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