Measures on circle coarse-grained systems of sets

Measures on circle coarse-grained systems of sets We show that a (non-negative) measure on a circle coarse-grained system of sets can be extended, as a (non-negative) measure, over the collection of all subsets of the circle. This result contributes to quantum logic probability (de Lucia in Colloq Math 80(1):147–154, 1999; Gudder in Quantum Probability, Academic Press, San Diego, 1988; Gudder in SIAM Rev 26(1):71–89, 1984; Harding in Int J Theor Phys 43(10):2149–2168, 2004; Navara and Pták in J Pure Appl Algebra 60:105–111, 1989; Pták in Proc Am Math Soc 126(7):2039–2046, 1998, etc.) and completes the analysis of coarse-grained measures carried on in De Simone and Pták (Bull Pol Acad Sci Math 54(1):1–11, 2006; Czechoslov Math J 57(132) n.2:737–746, 2007), Gudder and Marchand (Bull Pol Acad Sci Math 28(11–12):557–564, 1980) and Ovchinnikov (Construct Theory Funct Funct Anal 8:95–98, 1992). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Measures on circle coarse-grained systems of sets

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Publisher
SP Birkhäuser Verlag Basel
Copyright
Copyright © 2009 by Birkhäuser Verlag Basel/Switzerland
Subject
Mathematics; Econometrics; Calculus of Variations and Optimal Control; Optimization; Potential Theory; Operator Theory; Fourier Analysis
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-009-0015-6
Publisher site
See Article on Publisher Site

Abstract

We show that a (non-negative) measure on a circle coarse-grained system of sets can be extended, as a (non-negative) measure, over the collection of all subsets of the circle. This result contributes to quantum logic probability (de Lucia in Colloq Math 80(1):147–154, 1999; Gudder in Quantum Probability, Academic Press, San Diego, 1988; Gudder in SIAM Rev 26(1):71–89, 1984; Harding in Int J Theor Phys 43(10):2149–2168, 2004; Navara and Pták in J Pure Appl Algebra 60:105–111, 1989; Pták in Proc Am Math Soc 126(7):2039–2046, 1998, etc.) and completes the analysis of coarse-grained measures carried on in De Simone and Pták (Bull Pol Acad Sci Math 54(1):1–11, 2006; Czechoslov Math J 57(132) n.2:737–746, 2007), Gudder and Marchand (Bull Pol Acad Sci Math 28(11–12):557–564, 1980) and Ovchinnikov (Construct Theory Funct Funct Anal 8:95–98, 1992).

Journal

PositivitySpringer Journals

Published: May 12, 2009

References

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