An abstract treatment of the individual ergodic theorem
نویسندگان
چکیده
منابع مشابه
The Converse of the Individual Ergodic Theorem
converge almost everywhere to a finite limit f*(x). It then follows that the limit function/* is integrable and that/*(7x) =/*(x) almost everywhere. This result can be applied to certain cases in which the given measure m is not preserved by the transformation T. In order to discuss this application, we recall some terminology for measures and transformations. If (X, S) is a measurable space, a...
متن کاملStrongly Ergodic Sequences of Integers and the Individual Ergodic Theorem
Let S = {ki,ki, ...} be an increasing sequence of positive integers. We call S strongly ergodic if for every measure preserving transformation T on a probability space (Cl, J, P) and every / £ Li(f2) we have limn-»oo(l/n) J^^j f(TkiuJ) = Pf(w) a.e. where Pf is the appropriate limit guaranteed by the individual ergodic theorem. We give sufficient conditions for a sequence S to be strongly ergodi...
متن کاملIndividual ergodic theorem for intuitionistic fuzzy observables using intuitionistic fuzzy state
The classical ergodic theory hasbeen built on σ-algebras. Later the Individual ergodictheorem was studied on more general structures like MV-algebrasand quantum structures. The aim of this paper is to formulate theIndividual ergodic theorem for intuitionistic fuzzy observablesusing m-almost everywhere convergence, where m...
متن کاملIndividual Ergodic Theorem for Unitary Maps of Random Matrices
Using simple techniques of finite von Neumann algebras, we prove a limit theorem for random matrices. 1. Notation and main result 1.1. Let (Ω,F , μ) be a probability space, and let H denote the space of all d × d matrices with entries in the complex space L2(Ω, μ). H is a Hilbert space with the inner product (1) 〈AB〉 = Φ(AB∗), where φ(A) = ∫ Ω tr A(ω)μ(dμ), and tr denotes the normalized trace o...
متن کاملThe 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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1940
ISSN: 0386-2194
DOI: 10.3792/pia/1195579088