Representation theorem for convex effect algebras

Stanley P. Gudder; Sylvia Pulmannová

Commentationes Mathematicae Universitatis Carolinae (1998)

  • Volume: 39, Issue: 4, page 645-659
  • ISSN: 0010-2628

Abstract

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Effect algebras have important applications in the foundations of quantum mechanics and in fuzzy probability theory. An effect algebra that possesses a convex structure is called a convex effect algebra. Our main result shows that any convex effect algebra admits a representation as a generating initial interval of an ordered linear space. This result is analogous to a classical representation theorem for convex structures due to M.H. Stone.

How to cite

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Gudder, Stanley P., and Pulmannová, Sylvia. "Representation theorem for convex effect algebras." Commentationes Mathematicae Universitatis Carolinae 39.4 (1998): 645-659. <http://eudml.org/doc/248280>.

@article{Gudder1998,
abstract = {Effect algebras have important applications in the foundations of quantum mechanics and in fuzzy probability theory. An effect algebra that possesses a convex structure is called a convex effect algebra. Our main result shows that any convex effect algebra admits a representation as a generating initial interval of an ordered linear space. This result is analogous to a classical representation theorem for convex structures due to M.H. Stone.},
author = {Gudder, Stanley P., Pulmannová, Sylvia},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {effect algebras; convex structures; ordered linear spaces; effect algebras; convex structures; ordered linear spaces},
language = {eng},
number = {4},
pages = {645-659},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Representation theorem for convex effect algebras},
url = {http://eudml.org/doc/248280},
volume = {39},
year = {1998},
}

TY - JOUR
AU - Gudder, Stanley P.
AU - Pulmannová, Sylvia
TI - Representation theorem for convex effect algebras
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1998
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 39
IS - 4
SP - 645
EP - 659
AB - Effect algebras have important applications in the foundations of quantum mechanics and in fuzzy probability theory. An effect algebra that possesses a convex structure is called a convex effect algebra. Our main result shows that any convex effect algebra admits a representation as a generating initial interval of an ordered linear space. This result is analogous to a classical representation theorem for convex structures due to M.H. Stone.
LA - eng
KW - effect algebras; convex structures; ordered linear spaces; effect algebras; convex structures; ordered linear spaces
UR - http://eudml.org/doc/248280
ER -

References

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