Almost Everywhere Convergence II

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

Alexandra Bellow, Roger L. Jones

• Publisher: Academic Press
• Year: 2014
• ISBN:
  9781483265926
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

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

• Front Cover
• Almost Everywhere Convergence II
• Copyright Page
• Table of Contents
• CONTRIBUTORS
• CONFERENCE PARTICIPANTS
• Dedication
• Preface
• Chapter 1. A Solution to a Problem of A. Bellow
• Chapter 2. Universal Weights from Dynamical Systems To Mean–Bounded Positive Operators on Lp
• Chapter 3. SOME CONNECTIONS BETWEEN ERGODIC THEORY AND HARMONIC ANALYSIS
• Chapter 4. On Hopfs Ergodic Theorem for Particles with Different Velocities
• Chapter 5. A Note on the Strong Law of Large Numbers for Partial Sums of Independent Random Vectors
• Chapter 6. SUMMABILITY METHODS AND ALMOST-SURE CONVERGENCE
• Chapter 7. Concerning Induced Operators and Alternating Sequences
• Chapter 8. Maximal inequalities and ergodic theorems for Cesàro-α or weighted averages
• Chapter 9. THE HILBERT TRANSFORM OF THE GAUSSIAN
• Chapter 10. Mean Ergodicity of L1 Contractions and Pointwise Ergodic Theorems
• Chapter 11. Multi–Parameter Moving Averages
• Chapter 12. An Almost Sure Convergence Theorem For Sequences of Random Variables Selected From Log-Convex Sets
• Chapter 13. DIVERGENCE OF ERGODIC AVERAGES AND ORBITAL CLASSIFICATION OF NON-SINGULAR TRANSFORMATIONS
• Chapter 14. SOME ALMOST SURE CONVERGENCE PROPERTIES OF WEIGHTEDSUMS OF MARTINGALE DIFFERENCE SEQUENCES
• Chapter 15. Pointwise ergodic theorems for certain order preserving mappings in L1†
• Chapter 16. On the almost sure central limit theorem
• Chapter 17. UNIVERSALLY BAD SEQUENCES IN ERGODIC THEORY
• Chapter 18. On an Inequality of Kahane
• Chapter 19. A PRINCIPLE FOR ALMOST EVERYWHERE CONVERGENCE OF MULTIPARAMETER PROCESSES