Decompositions of measures on pseudo effect algebras

  title={Decompositions of measures on pseudo effect algebras},
  author={Anatolij Dvurecenskij},
  journal={Soft Computing},
Recently, in Dvurečenskij (, 2011), it was shown that if a pseudo effect algebra satisfies a kind of the Riesz decomposition property (RDP), then its state space is either empty or a nonempty simplex. This will allow us to prove a Yosida–Hewitt type and a Lebesgue type decomposition for measures on pseudo effect algebra with RDP. The simplex structure of the state space will entail not only the existence of such a decomposition but also its uniqueness. 

Involutive filters of pseudo-hoops

It is proved that in the case of good pseudo-hoops, the sets of fantastic and involutive filters are equal, and it is also proved that any implicative filter of a bounded Pseudo-hoop is involutive and that any Boolean filter of an bounded Wajsberg pseudo-Hoop is involuntary.

Bounded pseudo-hoops with internal states

State MV-algebras were introduced by Flaminio and Montagna as MV-algebras with internal states. Di Nola and Dvurečenskij presented the notion of state-morphism MV-algebra which is a stronger

Involutive filters of pseudo-hoops

In this paper, we introduce the notion of involutive filters of pseudo-hoops, and we emphasize their role in the probability theory on these structures. Characterizations of involutive pseudo-hoops



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We study states, measures, and signed measures on pseudo effect algebras with some version of the Riesz Decomposition Property (RDP). We show that the set of all Jordan signed measures is always an

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This paper is the continuation of the previous paper by Dvurečenskij and Vetterlein (2001), Int. J. Theor. Phys. 40(3). We show that any pseudoeffect algebra fulfilling a certain property of Riesz

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A partial binary operation which model the addition in pseudo MV-algebras is introduced and basic properties of such an addition are given.

Pseudo MV-algebras are intervals in ℓ-groups

  • A. Dvurecenskij
  • Mathematics
    Journal of the Australian Mathematical Society
  • 2002
Abstract We show that any pseudo MV-algebra is isomorphic with an interval Γ(G, u), where G is an ℓ-group not necessarily Abelian with a strong unit u. In addition, we prove that the category of

Central elements and Cantor-Bernstein's theorem for pseudo-effect algebras

  • A. Dvurecenskij
  • Mathematics
    Journal of the Australian Mathematical Society
  • 2003
Abstract Pseudo-effect algebras are partial algebras (E; +, 0, 1) with a partially defined addition + which is not necessary commutative and with two complements, left and right ones. We define

States on Pseudo MV-Algebras

It is proved that representable and normal-valued pseudo MV-algebras admit at least one state and it is shown that extremal states correspond to normal maximal ideals.

Finitely additive measures

0. Introduction. The present paper is concerned with real-valued measures which enjoy the property of finite additivity but not necessarily the property of countable additivity. Our interest in such

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The effects in a quantum-mechanical system form a partial algebra and a partially ordered set which is the prototypical example of the effect algebras discussed in this paper. The relationships among

New trends in quantum structures

Preface. Introduction. 1. D-posets and Effect Algebras. 2. MV-algebras and QMV-algebras. 3. Quotients of Partial Abelian Monoids. 4. Tensor Product of D-Posets and Effect Algebras. 5. BCK-algebras.