Probability in physics and a theorem on simultaneous observability

V. S. Varadarajan

pp. 171-203

in: Clifford A. Hooker (ed), The logico-algebraic approach to quantum mechanics I, Berlin, Springer, 1975

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.