Abstract
It is nearly thirty years since A. N. Kolmogorov explicitly wrote down the axioms of modern probability theory in his celebrated monograph [10]. During the intervening decades this theory has seen remarkable development, both in its theoretical and practical aspects. The diverse theories of mathematical statistics, the rapidly developing field of information theory, the applications to thermodynamics and statistical mechanics are only some of a long list of fields which are dominated to a substantial degree by probability theory. Moreover, many of the mathematical questions raised and answered by this theory have given deep and subtle insights into some difficult problems of analysis. One has only to mention the modern theory of Markov processes which has given new insights into such classical problems as boundary values and potential 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.
Bibliography
Baer, R., Linear Algebra and Projective Geometry, Academic Press, New York, 1952.
Birkhoff, G. Lattice Theory, Amer. Math. Soc. Colloq. Publ., 1948.
Birkhoff, G., and von Neuman, J., ‘The Logic of Quantum Mechanics’, Ann. of Math. 37 (1936), 823–843.
Feynman, R. P., ‘The Concept of Probability in Quantum Mechanics’, Proc. Second Berkeley Symposium in Mathematical Statistics and Probability, Berkeley, Calif., 1951, pp. 533–541.
Gleason, A. M., ‘Measures on the Closed Subspaces of a Hilbert Space’, J. Rat. Mech. Analysis 6 (1957), 885–894.
Halmos, P. R., Introduction to Hilbert Space and the Theory of Spectral Multiplicity, Chelsea Press, New York, 1957.
Halmos, P. R., Measure Theory, Von Nostrand, New York, 1950.
Halmos, P. R., ‘The Foundations of Probability’, Amer. Math. Monthly 51 (1944), 493–510.
Heisenberg, W., The Physical Principles of the Quantum Theory, Dover Publications, New York, 1930.
Kolmogorov, A. N., Grundbegriffe der Wahrscheinlichkeitsrechnung, Berlin, 1933.
Loomis, L. H., ‘On the Representation of σ-Complete Boolean Algebras’, Bull. Amer. Math. Soc. 53 (1947), 757–760.
Mackey, G. W., ‘Quantum Mechanics and Hilbert Space’, Amer. Math. Monthly 64 (1957), 45–57.
Mackey, G. W., The Mathematical Foundations of Quantum Mechanics, Harvard University, lecture notes, 1960.
Mackey, G. W., ‘Borel Structures in Groups and Their Duals’, Trans. Amer. Math. Soc. 85 (1957), 134–165.
Murray, F. J. and von Neumann, J., ‘On Rings of Operators’, Ann. of Math. 37 (1936), 116–229.
Murray, F. J., and von Neumann, J., ‘On Rings of Operators. IV, Ann. of Math. 44 (1943), 716–808.
von Neumann, J., Mathematical Foundations of Quantum Mechanics (transi, from the the German edition by R. T. Beyer), Princeton University Press, Princeton, 1955.
von Neumann, J., Continuous Geometry, Princeton University Press, Princeton, 1960.
von Neumann, J., ‘On Rings of Operators. Reduction Theory’, Ann. of Math. 50 (1949), 401–485.
Segal, I. E., ‘Abstract Probability Spaces and a Theorem of Kolmogoroff’, Amer. J. Math. 76 (1954), 721–732.
Segal, I. E., ‘Postulates for General Quantum Mechanics’, Ann. of Math. 48 (1947), 930–948.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1975 D. Reidel Publishing Company, Dordrecht, Holland
About this chapter
Cite this chapter
Varadarajan, V.S. (1975). Probability in Physics and a Theorem on Simultaneous Observability. In: Hooker, C.A. (eds) The Logico-Algebraic Approach to Quantum Mechanics. The University of Western Ontario Series in Philosophy of Science, vol 5a. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-1795-4_11
Download citation
DOI: https://doi.org/10.1007/978-94-010-1795-4_11
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-277-0613-3
Online ISBN: 978-94-010-1795-4
eBook Packages: Springer Book Archive