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Laws of large numbers and the central limit theorems on a logic. (English) Zbl 0419.60022

MSC:

60F05 Central limit and other weak theorems
60F15 Strong limit theorems
60B99 Probability theory on algebraic and topological structures
81P20 Stochastic mechanics (including stochastic electrodynamics)
03G12 Quantum logic
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References:

[1] ГНЄДЄНКО Б. В.: Курс тєории вєроятностєй. Москва 1965.
[2] GUDDER S. P.: Hilbert space, independence, and generalized probability. J. Math. Analysis and Appl., 20, 1, 1967, 48-61. · Zbl 0171.15602
[3] GUDDER S. P.: Uniqueness and existence properties of bounded observables. Pac. J. Math., 19, 1, 1966, 81-83. · Zbl 0149.23603
[4] ХАЛМОUI П. Р.: Тєория мєры. Москва 1953.
[5] HOLEVO A. S.: Statistical decision theory for quantum systems. J. Multivar. Anal., 3, 4, 1973, 337-394. · Zbl 0275.62004
[6] VARADARAJAN V. S.: Geometry of quantum theory. New York 1968. · Zbl 0155.56802
[7] VARADARAJAN V. S.: Probability in physics and a theorem on simultaneous observability. Comm. Pure appl. Math., 15, 1962, 189-217. · Zbl 0109.44705
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