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Order properties of the space of finitely additive transition functions. (Russian, English) Zbl 1053.46024
Sib. Mat. Zh. 45, No. 1, 80-102 (2004); translation in Sib. Math. J. 45, No. 1, 69-85 (2004).
The basic order properties, as well as some metric and algebraic properties, of the set of finitely additive transition functions on an arbitrary measurable space are studied, as endowed with the structure of an ordered normed algebra, and some connections with the classical spaces of linear operators, vector measures, and measurable vector-valued functions are revealed. In particular, the question of splitting the space of transition functions into the sum of the subspaces of countably additive and purely finitely additive transition functions is examined.
46G10 Vector-valued measures and integration
47B37 Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
47B38 Linear operators on function spaces (general)
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
60J35 Transition functions, generators and resolvents
28A10 Real- or complex-valued set functions
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