Abstract
In this communication the notion of the independence of observables in a state on a logic, as it was introduced Gudder (1967), will be studied. Some generalized forms of the weak law of large numbers and the central limit theorems for observables of a logic will be proved. The used methods are similar to those of the conventional probability theory.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
GNEDENKO, B.V. (1965): Kurs teorii verojatnostej, Moskva.
GUDDER, S.P. (1966): Uniqueness and existence properties of bounded observables. In:Pac.J.Math.Analys. and Appl., 19,1,(1966) 81–93.
GUDDER, S.P. (1967) Hilbert space, independence, and generalized probability. In. J. Math. Analysis and Appl. 20,1, (1967) 48–61.
HALMOS, P.R. (1953) Teorija mery, Moskva(1953).
HOLEYO, A.S. (1973): Statistical decision theory for quantum systems. In; J. Multivar. Anal., 3,4(1973) 337–394.
VARADARAJAN, V.S. (1962)•Probability in physics and a theorem on simultaneous observability. In: Comm. Pure Appl.Math. 15,(1962) 189–217.
VARADARAJAN, V.S. (1968)Geometry of quantum theory. New York (1968).
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1978 ACADEMIA, Publishing House of the Czechoslovak Academy of Sciences, Prague
About this chapter
Cite this chapter
Dvurečenskij, A. (1978). Remark on the Laws of Large Numbers and the Central Limit Theorems on a Logic. In: Transactions of the Eighth Prague Conference. Czechoslovak Academy of Sciences, vol 8A. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-9857-5_15
Download citation
DOI: https://doi.org/10.1007/978-94-009-9857-5_15
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-009-9859-9
Online ISBN: 978-94-009-9857-5
eBook Packages: Springer Book Archive