Lectures on Ergodic Theory

by Paul R. Halmos

Overview

2013 Reprint of 1956 Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. Ergodic theory is a branch of mathematics that studies dynamical systems with an invariant measure and related problems. Its initial development was motivated by problems of statistical physics. A central concern of ergodic theory is the behavior of a dynamical system when it is allowed to run for a long time. Paul Richard Halmos (1916 - 2006) was a Hungarian-born American mathematician who made fundamental advances in the areas of probability theory, statistics, operator theory, ergodic theory, and functional analysis (in particular, Hilbert spaces). He was also recognized as a great mathematical expositor.

Product Details

ISBN-13:	9781614274612
Publisher:	Martino Fine Books
Publication date:	08/07/2013
Pages:	110
Product dimensions:	6.00(w) x 9.00(h) x 0.26(d)

About the Author

Hungarian-born Paul R. Halmos (1916–2006) is widely regarded as a top-notch expositor of mathematics. He taught at the University of Chicago and the University of Michigan as well as other universities and made significant contributions to several areas of mathematics including mathematical logic, probability theory, ergodic theory, and functional analysis.

Table of Contents

Introduction
Examples
Recurrence
Mean convergence
Pointwise convergence
Comments on the ergodic theorem
Mixing
Measure algebras
Discrete spectrum
Automorphisms of compact groups
Generalized proper values
Weak topology
Weak approximation
Uniform topology
Uniform approximation
Category
Invariant measures
Invariant measures: the solution
Invariant measures: the problem
Generalized ergodic theorems
Unsolved problems
References