Almost Everywhere Convergence II

Almost Everywhere Convergence II

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

1st Edition - August 28, 1991

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  • Editors: Alexandra Bellow, Roger L. Jones
  • eBook ISBN: 9781483265926

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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

  • Contributors




    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

Product details

  • No. of pages: 288
  • Language: English
  • Copyright: © Academic Press 1991
  • Published: August 28, 1991
  • Imprint: Academic Press
  • eBook ISBN: 9781483265926

About the Editors

Alexandra Bellow

Roger L. Jones

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