Probability in Banach Spaces 6: "Proceedings Of The Sixth International Conference, Sandbjerg, Denmark 1986"

This volume contains a selection of papers by the participants of the 6. International Conference on Probability in Banach Spaces, Sand­ bjerg, Denmark, June 16-D1, 1986. The conference was attended by 45 participants from several countries. One thing makes this conference completely different from the previous five ones, namely that it was ar­ ranged jointly in Probability in Banach spaces and Banach space theory with almost equal representation of scientists in the two fields. Though these fields are closely related it seems that direct collaboration between researchers in the two groups has been seldom. It is our feeling that the conference, where the participants were together for five days taking part in lectures and intense discussions of mutual problems, has contributed to a better understanding and closer collaboration in the two fields. The papers in the present volume do not cover all the material pre­ sented in the lectures; several results covered have been published else­ where. The sponsors of the conference are: The Carlsberg Foundation, The Danish Natural Science Research Council, The Danish Department of Education, The Department of Mathematics, Odense University, The Department of Mathematics, Aarhus University, The Knudsen Foundation, Odense, Odense University, The Research Foundation of Aarhus University, The Thborg Foundation. The participants and the organizers would like to thank these institu­ tions for their support. The Organizers. Contents A. de Acosta and M. Ledoux, On the identification of the limits in the law of the iterated logarithm in Banach spaces..... This Volume Contains A Selection Of Papers By The Participants Of The 6. International Conference On Probability In Banach Spaces, Sand Bjerg, Denmark, June 16-d1, 1986. The Conference Was Attended By 45 Participants From Several Countries. One Thing Makes This Conference Completely Different From The Previous Five Ones, Namely That It Was Ar Ranged Jointly In Probability In Banach Spaces And Banach Space Theory With Almost Equal Representation Of Scientists In The Two Fields. Though These Fields Are Closely Related It Seems That Direct Collaboration Between Researchers In The Two Groups Has Been Seldom. It Is Our Feeling That The Conference, Where The Participants Were Together For Five Days Taking Part In Lectures And Intense Discussions Of Mutual Problems, Has Contributed To A Better Understanding And Closer Collaboration In The Two Fields. The Papers In The Present Volume Do Not Cover All The Material Pre Sented In The Lectures; Several Results Covered Have Been Published Else Where. The Sponsors Of The Conference Are: The Carlsberg Foundation, The Danish Natural Science Research Council, The Danish Department Of Education, The Department Of Mathematics, Odense University, The Department Of Mathematics, Aarhus University, The Knudsen Foundation, Odense, Odense University, The Research Foundation Of Aarhus University, The Thborg Foundation. The Participants And The Organizers Would Like To Thank These Institu Tions For Their Support. The Organizers. Contents A. De Acosta And M. Ledoux, On The Identification Of The Limits In The Law Of The Iterated Logarithm In Banach Spaces. . . . . This volume contains a selection of papers by the participants of the 6. International Conference on Probability in Banach Spaces, SandƯ bjerg, Denmark, June 16-D1, 1986. The conference was attended by 45 participants from several countries. One thing makes this conference completely different from the previous five ones, namely that it was arƯ ranged jointly in Probability in Banach spaces and Banach space theory with almost equal representation of scientists in the two fields. Though these fields are closely related it seems that direct collaboration between researchers in the two groups has been seldom. It is our feeling that the conference, where the participants were together for five days taking part in lectures and intense discussions of mutual problems, has contributed to a better understanding and closer collaboration in the two fields. The papers in the present volume do not cover all the material preƯ sented in the lectures; several results covered have been published elseƯ where. The sponsors of the conference are: The Carlsberg Foundation, The Danish Natural Science Research Council, The Danish Department of Education, The Department of Mathematics, Odense University, The Department of Mathematics, Aarhus University, The Knudsen Foundation, Odense, Odense University, The Research Foundation of Aarhus University, The Thborg Foundation. The participants and the organizers would like to thank these instituƯ tions for their support. The Organizers. Contents A. de Acosta and M. Ledoux, On the identification of the limits in the law of the iterated logarithm in Banach spaces. .. Content: Front Matter....Pages i-x On the identification of the limits in the law of the iterated logarithm in Banach spaces....Pages 1-12 Analytic and Empirical Evidences of Isoperimetric Processes....Pages 13-40 Weak convergence of vector valued martingales....Pages 41-50 Fonctions aléatoires � valeurs vectorielles....Pages 51-81 On Functional Limit Theorems for a Class of Stochastic Processes Indexed by Pseudo-Metric Parameter Spaces (with applications to empirical processes)....Pages 82-100 Random Martingale Transform Inequalities....Pages 101-119 On Random Multipliers in the Central Limit Theorem with p-stable Limit, 0 < p < 2....Pages 120-149 Some Probability and Entropy Estimates for Gaussian Measures....Pages 150-156 Isometries of L p (X) and Vector Valued Ergodic Theorems....Pages 157-161 Some Exponential Inequalities with Applications to the Central Limit Theorem in C[0,1]....Pages 162-184 Extreme Values and LIL Behavior....Pages 185-218 Entropy Numbers and Duality for Operators with Values in a Hilbert Space....Pages 219-233 On the Convergence of Types for Radon Probability Measures in Banach Spaces....Pages 234-251 Gelfand Numbers and Euclidean Sections of Large Dimensions....Pages 252-264 The Law of the Iterated Logarithm for Empirical Processes....Pages 265-282 Universal Donsker Classes and Type 2....Pages 283-288 Back Matter....Pages 289-289