2,474 research outputs found
MV-algebras, multiple bets and subjective states
AbstractIn this paper MV-algebras, the algebras of LĢµukasiewicz infinite-valued logics, are interpreted in a structure of bets, and a subjective interpretation of finitely additive measures on MV-algebras is given
Representation of States on Effect-Tribes and Effect Algebras by Integrals
We describe -additive states on effect-tribes by integrals.
Effect-tribes are monotone -complete effect algebras of functions where
operations are defined by points. Then we show that every state on an effect
algebra is an integral through a Borel regular probability measure. Finally, we
show that every -convex combination of extremal states on a monotone
-complete effect algebra is a Jauch-Piron state.Comment: 20 page
Smearing of Observables and Spectral Measures on Quantum Structures
An observable on a quantum structure is any -homomorphism of quantum
structures from the Borel -algebra of the real line into the quantum
structure which is in our case a monotone -complete effect algebras
with the Riesz Decomposition Property. We show that every observable is a
smearing of a sharp observable which takes values from a Boolean
-subalgebra of the effect algebra, and we prove that for every element
of the effect algebra there is its spectral measure
States on pseudo effect algebras and integrals
We show that every state on an interval pseudo effect algebra satisfying
some kind of the Riesz Decomposition Properties (RDP) is an integral through a
regular Borel probability measure defined on the Borel -algebra of a
Choquet simplex . In particular, if 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.
Loomis--Sikorski Theorem and Stone Duality for Effect Algebras with Internal State
Recently Flaminio and Montagna, \cite{FlMo}, extended the language of
MV-algebras by adding a unary operation, called a state-operator. This notion
is introduced here also for effect algebras. Having it, we generalize the
Loomis--Sikorski Theorem for monotone -complete effect algebras with
internal state. In addition, we show that the category of divisible
state-morphism effect algebras satisfying (RDP) and countable interpolation
with an order determining system of states is dual to the category of Bauer
simplices such that is an F-space
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