Abstract
In this paper we formulate and prove analogues of the Hahn-Jordan decomposition and an Andô-Douglas-Radon-Nikodým theorem in Dedekind complete Riesz spaces with a weak order unit, in the presence of a Riesz space conditional expectation operator. As a consequence we can characterize those subspaces of the Riesz space which are ranges of conditional expectation operators commuting with the given conditional expectation operators and which have a larger range space. This provides the first step towards a formulation of Markov processes on Riesz spaces.
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This work was supported in part by the Centre for Applicable Analysis and Number Theory and by South African National Research Foundation grant FA2007041200006.
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Watson, B.A. An Andô-Douglas type theorem in Riesz spaces with a conditional expectation. Positivity 13, 543–558 (2009). https://doi.org/10.1007/s11117-008-2239-2
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DOI: https://doi.org/10.1007/s11117-008-2239-2