Decompositions of substochastic transition functions

Lange, Kenneth

doi:10.1090/S0002-9939-1973-0314124-4

Decompositions of substochastic transition functions
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Proc. Amer. Math. Soc. 37 (1973), 575-580 Request permission

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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