The Vitali-Hahn-Saks theorem for the product of quantum logics

• Autorzy: De Simone A. , Navara M. , Pták P.
• Języki publikacji: EN

Abstrakty

EN

We show as a main result that if each quantum logic of a given collection of quantum logics satisfies the Vitali-Hahn-Saks theorem, then so does their product. As a consequence we formulate a dual result for the sum of a collection of Dynkin systems.

Słowa kluczowe

EN

quantum logic; Vitali-Hahn-Saks theorem; Dynkin system

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2002
• Tom: Vol. 35, nr 4
• Strony: 717--725
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

De Simone A.

• Dipartimento di Matematica e Statistica, Università Degli Studi di Napoli "Federico II", 80126 Napoli, Italy

autor

Navara M.

• Center for Machine Perception, Department of Cybernetics, Faculty of Electrical Engineering, Czech Technical University, Technická 2, 166 27 Prague 6, Czech Republic

autor

Pták P.

• Department of Mathematics, Faculty of Electrical Engineering, Czech Technical University, Technická 2, 166 27 Prague 6, Czech Republic

Bibliografia

• [1] C. D. Aliprantis, K. C. Border, Infinite Dimensional Analysis, Springer Verlag, 1994.
• [2] H. Bauer, Probability Theory and Elements of Measure Theory, Academic Press, London, 1981.
• [3] S. Gudder, Stochastic Methods in Quantum Mechanics, Elsevier/North-Holland, Amsterdam, 1979.
• [4] P. de Lucia, Convergence theorems in orthomodular posets, Atti Sem. Mat. Fis. Modena, Suppl. 44 (1998), 171-179.
• [5] A. De Simone, Absolute continuity of states on concrete logics, Int. J. Theor. Phys. 39 (2000), 615-620.
• [6] A. Dvurečenskij, On convergence of signed states, Math. Slovaca 28 (1978), 289-295.
• [7] K. Hrbáček, T. Jech, Introduction to Set Theory, 3rd Edition, Marcel Dekker, New York, 1999.
• [8] V. Maňasová, P. Pták, On states on the product of logics, Int. J. Theor. Phys. 20 (1981), 451-457.
• [9] J. Neuven, Bases mathématique du calcul des probabilités, Paris, Masson et Cil, 1964.
• [10] V. Palko, On the convergence and absolute continuity of signed states on a logic, Math. Slovaca 35 (1985), 267-275.
• [11] P. Pták, Concrete quantum logics, Int. J. Theor. Phys. 39 (2000), 827-837.
• [12] P. Pták, S. Pulmannová, Orthomodular Structures as Quantum Logics, Kluwer Acad. Publ., Dordrecht/Boston/London 1991.