منابع مشابه
The Ergodic Theorem
Measure-preserving systems arise in a variety of contexts, such as probability theory, information theory, and of course in the study of dynamical systems. However, ergodic theory originated from statistical mechanics. In this setting, T represents the evolution of the system through time. Given a measurable function f : X → R, the series of values f(x), f(Tx), f(T x)... are the values of a phy...
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With these assumptions we have T defined for every integer n as a 1-1, onto, bimeasurable transformation. Henceforth we shall assume that every set considered is measurable, i.e. an element of a. We shall say that P is invariant if P(A) =P(TA) for every set A, P is ergodic if P is invariant and if P(U^L_oo TA) = 1 for every set A for which P(A) > 0 , and finally P is strongly mixing if P is inv...
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Recently, the investigation of the ergodic properties of quantum dynamical systems had a considerable growth. Since the theory of quantum dynamical systems provides convenient mathematical description of the irreversible dynamics of an open quantum system (see [9], sec.4.3, [31],[27]). In this setting, the matter is more complicated than in the classical case. Some differences between classical...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1965
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1965-0174705-8