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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Decompositions of substochastic transition functions


Author: Kenneth Lange
Journal: Proc. Amer. Math. Soc. 37 (1973), 575-580
MSC: Primary 60J35
MathSciNet review: 0314124
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Abstract: Three decompositions of a substochastic transition function are shown to yield substochastic parts. These are the Lebesgue decomposition with respect to a finite measure, the decomposition into completely atomic and continuous parts, and on $ {R^n}$, a decomposition giving a part with continuous distribution function and a part with discontinuous distribution function.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0314124-4
Keywords: Substochastic transition function, space of measures, Lebesgue decomposition, atom, distribution function, Fell topology
Article copyright: © Copyright 1973 American Mathematical Society