Almost Everywhere Convergence II - 1st Edition - ISBN: 9780120855209, 9781483265926

Almost Everywhere Convergence II

1st Edition

Proceedings of the International Conference on Almost Everywhere Convergence in Probability and Ergodic Theory, Evanston, Illinois, October 16–20, 1989

Editors: Alexandra Bellow Roger L. Jones
eBook ISBN: 9781483265926
Imprint: Academic Press
Published Date: 28th August 1991
Page Count: 288
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Almost Everywhere Convergence II presents the proceedings of the Second International Conference on Almost Everywhere Convergence in Probability and Ergodotic Theory, held in Evanston, Illinois on October 16–20, 1989. This book discusses the many remarkable developments in almost everywhere convergence.

Organized into 19 chapters, this compilation of papers begins with an overview of a generalization of the almost sure central limit theorem as it relates to logarithmic density. This text then discusses Hopf's ergodic theorem for particles with different velocities. Other chapters consider the notion of a log–convex set of random variables, and proved a general almost sure convergence theorem for sequences of log–convex sets. This book discusses as well the maximal inequalities and rearrangements, showing the connections between harmonic analysis and ergodic theory. The final chapter deals with the similarities of the proofs of ergodic and martingale theorems.

This book is a valuable resource for mathematicians.

Table of Contents





A Solution to a Problem of A. Bellow

Universal Weights from Dynamical Systems to Mean—Bounded Positive Operators on LP

Some Connections Between Ergodic Theory and Harmonic Analysis

On Hopf's Ergodic Theorem for Particles with Different Velocities

A Note on the Strong Law of Large Numbers for Partial Sums of Independent Random Vectors

Summability Methods and Almost-sure Convergence

Concerning Induced Operators and Alternating Sequences

Maximal Inequalities and Ergodic Theorems for Cesàro—α or Weighted Averages

The Hilbert Transform of the Gaussian

Mean Ergodicity of L1 Contractions and Pointwise Ergodic Theorems

Multi—Parameter Moving Averages

An Almost Sure Convergence Theorem for Sequences of Random Variables Selected from Log—Convex Sets

Divergence of Ergodic Averages and Orbital Classification of Non—singular Transformations

Some Almost Sure Convergence Properties of Weighted Sums of Martingale Difference Sequences

Pointwise Ergodic Theorems for Certain Order Preserving Mappings in L1

On the Almost Sure Central Limit Theorem

Universally Bad Sequences in Ergodic Theory

On an Inequality of Kahane

A Principle for Almost Everywhere Convergence of Multiparameter Processes


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© Academic Press 1991
Academic Press
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About the Editor

Alexandra Bellow

Roger L. Jones

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