Displaying similar documents to “On Kalmbach measurability”

A measure-theoretic characterization of Boolean algebras among orthomodular lattices

Pavel Pták, Sylvia Pulmannová (1994)

Commentationes Mathematicae Universitatis Carolinae

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We investigate subadditive measures on orthomodular lattices. We show as the main result that an orthomodular lattice has to be distributive (=Boolean) if it possesses a unital set of subadditive probability measures. This result may find an application in the foundation of quantum theories, mathematical logic, or elsewhere.

On the structure of numerical event spaces

Gerhard Dorfer, Dietmar W. Dorninger, Helmut Länger (2010)

Kybernetika

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The probability p ( s ) of the occurrence of an event pertaining to a physical system which is observed in different states s determines a function p from the set S of states of the system to [ 0 , 1 ] . The function p is called a numerical event or multidimensional probability. When appropriately structured, sets P of numerical events form so-called algebras of S -probabilities. Their main feature is that they are orthomodular partially ordered sets of functions p with an inherent full set of states....

On joint distribution in quantum logics. I. Compatible observables

Anatolij Dvurečenskij (1987)

Aplikace matematiky

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The notion of a joint distribution in σ -finite measures of observables of a quantum logic defined on some system of σ -independent Boolean sub- σ -algebras of a Boolean σ -algebra is studied. In the present first part of the paper the author studies a joint distribution of compatible observables. It is shown that it may exists, although a joint obsevable of compatible observables need not exist.

Some problems for measures on non-standard algebraic structures

Maria Gabriella Graziano (2000)

Bollettino dell'Unione Matematica Italiana

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Nell'ultimo ventennio tutta una serie di lavori è stata rivolta allo studio delle misure su strutture algebriche più generali delle algebre di Boole, come i poset e i reticoli ortomodulari, le effect algebras, le BCK-algebras. La teoria così ottenuta interessa l'analisi funzionale, il calcolo delle probabilità e la topologia, più recentemente la teoria delle decisioni. Si presentano alcuni risultati relativi a misure su strutture algebriche non-standard analizzando, in particolare, gli...