On the structure of numerical event spaces

Title:

On the structure of numerical event spaces

Creator:

Dorfer, Gerhard, Dorninger, Dietmar, and Länger, Helmut

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:89d356ec-806b-4371-8044-c0d68bcefe60
uuid:89d356ec-806b-4371-8044-c0d68bcefe60

Subject:

orthomodular poset, full set of states, and numerical event

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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. A classical physical system can be characterized by the fact that the corresponding algebra P of S-probabilities is a Boolean lattice. We give necessary and sufficient conditions for systems of numerical events to be a lattice and characterize those systems which are Boolean. Assuming that only a finite number of measurements is available our focus is on finite algebras of S-probabilties.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

[971]-981

Source:

Kybernetika | 2010 Volume:46 | Number:6

Harvested from:

CDK

Metadata only:

false