Dvurečenskij, Anatolij Gleason theorem for signed measures with infinite values. (English) Zbl 0584.46053 Math. Slovaca 35, 319-325 (1985). The Gleason theorem for signed measures with infinite values on the lattice of all closed subspaces of a Hilbert space whose dimension is a nonreal measurable cardinal number \(\neq 2\) is proved. Cited in 5 Documents MSC: 46L51 Noncommutative measure and integration 46L53 Noncommutative probability and statistics 46L54 Free probability and free operator algebras 06C20 Complemented modular lattices, continuous geometries Keywords:Gleason theorem for signed measures with infinite values on the lattice of all closed subspaces of a Hilbert space whose dimension is a nonreal measurable cardinal number \(\neq 2\) PDFBibTeX XMLCite \textit{A. Dvurečenskij}, Math. Slovaca 35, 319--325 (1985; Zbl 0584.46053) Full Text: EuDML References: [1] DRISCH T.: Generalization of Gleason’s theorem. Inter. J. Theor. Phys., 18, 1979, 4, 239-243. · Zbl 0452.46036 · doi:10.1007/BF00671760 [2] DVUREČENSKIJ A.: Signed measures on a logic. Math. Slovaca, 28, 1978, 1, 33-40. [3] DVUREČENSKIJ A.: On convergence of signed states. Math. Slovaca, 21, 1978, 3, 289-295. [4] EILERS M., HORST E.: The theorem of Gleason for nonseparable Hilbert spaces. Inter. J. Theor. Phys. 13, 1975, 6, 419-424. · Zbl 0345.46021 · doi:10.1007/BF01808324 [5] GLEASON A. M.: Measures on the closed substaces of a Hilbert space. J. Math. Mech. 6,1957, 6, 885-893. · Zbl 0078.28803 [6] ШЄРСТНЄВ А. Н., ЛУГОВАЯ Г. Д.: О тєорємє Глизона для нєограничєнных мєр. Изв. Вузов. Матєм. 1980, Ho. 12, 30-32. [7] ШЄРСТНЄВ А. Н.: О прєдставлєнии мєр, заданных на ортопроєкторах пространства Гильбєрта, билинєйными формами. Изв. Вузов. Матєм., 1970, \? 9, 90-97. [8] ШЄРСТНЄВ А. Н.: О понятии заряда в нєкоммутативной схємє тєории мєры. Вєроятностныє мєтоды и кибєрнєтика, ЈЧд3 10-11, Казань, КГЧ, 1974, 68-72. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.