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).
Positivity – Springer Journals
Published: May 12, 2009
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