Complete transitivity and the ergodic principle
E Hopf - Proceedings of the National Academy of Sciences, 1932 - National Acad Sciences
ff(P)di Page 1 MATHEMATICS: E. HOPF COMPLETE TRANSITIVITY AND THE ERGODIC
PRINCIPLE By EBERHARD HOPF1 HARVARD COLLEGE OBSERVATORY Communicated …
PRINCIPLE By EBERHARD HOPF1 HARVARD COLLEGE OBSERVATORY Communicated …
[图书][B] Ergodic theory—introductory lectures
P Walters - 2007 - books.google.com
These are notes of a one-semester introductory course on Ergodic Theory that I gave at the
University of Maryland in College Park during the fall of 1970. I assumed the audience had …
University of Maryland in College Park during the fall of 1970. I assumed the audience had …
On the ergodic theorems
P Hartman - American Journal of Mathematics, 1947 - JSTOR
194 PHILIP IIARTMAN. product space of Q and the line-oo< t< oo, where measure on the
line is the ordinary Lebesgue measure. If these assumptions are satisfied and if a zero set of …
line is the ordinary Lebesgue measure. If these assumptions are satisfied and if a zero set of …
[图书][B] Ergodic theory
K Jacobs - 1962 - academic.oup.com
Ergodic theory is a subject which, having its roots in statistical mechanics, has become an
important branch of pure mathematics, with strong connections with functional analysis and …
important branch of pure mathematics, with strong connections with functional analysis and …
The recurrence theorem
FB Wright - A Century of Mathematics: Through the Eyes of the …, 1996 - books.google.com
The purpose of this note is to give a completely self-contained account of the recurrence
theorem of ergodic theory. This theorem was first proved by Poincaré, and, in modern form …
theorem of ergodic theory. This theorem was first proved by Poincaré, and, in modern form …
Abstract ergodic theorems
AI Tulcea, CI Tulcea - … of the National Academy of Sciences, 1962 - National Acad Sciences
1. Let (Z.£,, be a complete totally a-finite measure space and E a Banach space. For each 1<
p< o denote by 4C. the vector space of all (Bochner) measur-able mappings f of Z into E for …
p< o denote by 4C. the vector space of all (Bochner) measur-able mappings f of Z into E for …
On orbits under ergodic measure-preserving transformations
D Maharam - Transactions of the American Mathematical Society, 1965 - ams.org
1. Introduction. If a transformation T (from a space to itself) is given, two natural questions
arise. First, what properties does the orbit (2) of a general point have? Secondly, to what …
arise. First, what properties does the orbit (2) of a general point have? Secondly, to what …
Measure-preserving homeomorphisms and metrical transitivity
JC Oxtoby, SM Ulam - Annals of Mathematics, 1941 - JSTOR
In the study of dynamical systems one is led naturally to the consideration of measure-
preserving transformations. A Hamiltonian system of 2n differential equations induces in the …
preserving transformations. A Hamiltonian system of 2n differential equations induces in the …
Some generalizations of the ergodic theorem
HR Pitt - … Proceedings of the Cambridge Philosophical Society, 1942 - cambridge.org
Throughout this paper we shall suppose that denotes a set of elements x in which a
Lebesgue measure is defined and that itself is measurable and has finite measure. A (1, 1) …
Lebesgue measure is defined and that itself is measurable and has finite measure. A (1, 1) …
What is the ergodic theorem?
GD Birkhoff - The American Mathematical Monthly, 1942 - Taylor & Francis
What is the Ergodic Theorem? Page 1 WHAT IS THE ERGODIC THEOREM? GD BIRKHOFF,
Harvard University The integral of Lebesgue (1901), founded upon Borel measure, has been a …
Harvard University The integral of Lebesgue (1901), founded upon Borel measure, has been a …