States on Pseudo Effect Algebras and Integrals

Foundations of Physics 41 (7):1143-1162 (2011)
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Abstract

We show that every state on an interval pseudo effect algebra E satisfying an appropriate version of the Riesz Decomposition Property (RDP for short) is an integral through a regular Borel probability measure defined on the Borel σ-algebra of a Choquet simplex K. In particular, if E satisfies the strongest type of RDP, the representing Borel probability measure can be uniquely chosen to have its support in the set of the extreme points of K

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10.1007/s10701-011-9537-4

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Citations of this work

Kite Pseudo Effect Algebras.Anatolij Dvurečenskij - 2013 - Foundations of Physics 43 (11):1314-1338.
Module Structure on Effect Algebras.Simin Saidi Goraghani & Rajab Ali Borzooei - 2020 - Bulletin of the Section of Logic 49 (3):269-290.

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References found in this work

Effect algebras and unsharp quantum logics.D. J. Foulis & M. K. Bennett - 1994 - Foundations of Physics 24 (10):1331-1352.
States on pseudo MV-Algebras.Anatolij Dvurečenskij - 2001 - Studia Logica 68 (3):301-327.
Phi-symmetric effect algebras.M. K. Bennett & D. J. Foulis - 1995 - Foundations of Physics 25 (12):1699-1722.

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