Almost everywhere convergence II : proceedings of the International Conference on Almost Everywhere Convergence in Probability and Ergodic Theory in Evanston, Illinois October 16-20, 1989

Almost Everywhere Convergence II contains selected papers form the Second International conference on Almost Everywhere convergence in Probability and Ergodic Theory, which took place on October 16-20, 1989 at Northwestern University. It contains survey papers and major original contributions and should appeal to researchers in the area of ergodic theory and harmonic analysis as well as to graduate students entering these fields of study Content: Front Matter, Page iii Copyright, Page iv CONTRIBUTORS, Pages vii-viii CONFERENCE PARTICIPANTS, Page ix Dedication, Page xi Preface, Pages xiii-xiv A Solution to a Problem of A. Bellow, Pages 1-7, M.A. Akcoglu, A. del Junco, W.M.F. Lee Universal Weights from Dynamical Systems To Mean-Bounded Positive Operators on Lp, Pages 9-16, Idris Assani SOME CONNECTIONS BETWEEN ERGODIC THEORY AND HARMONIC ANALYSIS, Pages 17-40, Idris Assani, Karl Petersen, Homer White On Hopf's Ergodic Theorem for Particles with Different Velocities, Pages 41-47, Alexandra Bellow, Ulrich Krengel A Note on the Strong Law of Large Numbers for Partial Sums of Independent Random Vectors, Pages 49-68, Erich Berger SUMMABILITY METHODS AND ALMOST-SURE CONVERGENCE, Pages 69-83, N.H. Bingham, L.C.G. Rogers Concerning Induced Operators and Alternating Sequences, Pages 85-92, R.E. Bradley Maximal inequalities and ergodic theorems for Cesàro-α or weighted averages, Pages 93-107, M. Broise, Y. Déniel, Y. Derriennic THE HILBERT TRANSFORM OF THE GAUSSIAN, Pages 109-112, A.P. Calderón, Y. Sagher Mean Ergodicity of L1 Contractions and Pointwise Ergodic Theorems, Pages 113-126, Doan Çömez, Michael Lin Multi–Parameter Moving Averages, Pages 127-149, Roger L. Jones, James Olsen An Almost Sure Convergence Theorem For Sequences of Random Variables Selected From Log-Convex Sets, Pages 151-166, John C. Kieffer DIVERGENCE OF ERGODIC AVERAGES AND ORBITAL CLASSIFICATION OF NON-SINGULAR TRANSFORMATIONS, Pages 167-178, I. Kornfeld SOME ALMOST SURE CONVERGENCE PROPERTIES OF WEIGHTED SUMS OF MARTINGALE DIFFERENCE SEQUENCES, Pages 179-190, Tze Leung Lai Pointwise ergodic theorems for certain order preserving mappings in L1, Pages 191-207, MICHAEL LIN, RAINER WITTMANN On the almost sure central limit theorem, Pages 209-225, M. Peligrad, P. Révész UNIVERSALLY BAD SEQUENCES IN ERGODIC THEORY, Pages 227-245, Joseph Rosenblatt On an Inequality of Kahane, Pages 247-251, Yoram Sagher, Kecheng Zhou A PRINCIPLE FOR ALMOST EVERYWHERE CONVERGENCE OF MULTIPARAMETER PROCESSES, Pages 253-273, Louis Sucheston, László I. Szabó 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. Focusing on recent developments in almost everywhere convergence, this text contains survey papers and original contributions and is aimed at researchers in the field of ergodic theory and harmonic analysis, as well as graduate students entering these fields of study.