Independent Random Variables and Rearrangement Invariant Spaces (London Mathematical Society Lecture Note Series, Series Number 194)

The Subject Of This Book Lies On The Boundary Between Probability Theory And The Theory Of Function Spaces. Here Professor Braverman Investigates Independent Random Variables In Rearrangement Invariant (r.i.) Spaces. The Significant Feature Of R.i. Spaces Is That The Norm Of An Element Depends On Its Distribution Only, And This Property Allows The Results And Methods Associated With R.i. Spaces To Be Applied To Problems In Probability Theory. On The Other Hand, Probabilistic Methods Can Also Prove Useful In The Study Of R.i. Spaces. In This Book New Techniques Are Used And A Number Of Interesting Results Are Given. Most Of The Results Are Due To The Author But Have Never Before Been Available In English. Here They Are All Presented Together In A Volume That Will Be Essential Reading For All Serious Researchers In This Area. Michael Sh. Braverman. Includes Bibliographical References (p. [113]-115) And Index. Title Page......Page 3 Copyright......Page 4 CONTENTS......Page 5 Preface......Page 7 1. Rearrangement invariant spaces......Page 9 2. The function of dilatation and Boyd indices......Page 12 3. Independent random variables......Page 13 4. Probability inequalities......Page 15 5. Disjoint random variables......Page 16 6. The Kruglov property......Page 18 7. Bases and sequence spaces......Page 25 8. Stable distributions......Page 27 1. Rosenthal's inequality and a characterization of the spaces LP......Page 29 2. Estimates of von Bahr-Esseen type......Page 41 3. Upper estimates of the Rosenthal type......Page 46 4. Estimates in exponential Orlicz spaces......Page 50 1. 4-estimates (q# 2)......Page 58 2. 12-estimates......Page 78 3. Stable random variables with different exponents......Page 85 4. Equidistributed random variables in exponential Orlicz spaces......Page 91 1. Subspaces generated by bounded random variables......Page 96 2. Subspaces generated by equidistributed random variables......Page 112 References......Page 121 Index......Page 124 The subject of this book lies on the boundary between probability theory and the theory of function spaces. Here Professor Braverman investigates independent random variables in rearrangement invariant (r.i.) spaces. The significant feature of r.i. spaces is that the norm of an element depends on its distribution only, and this property allows the results and methods associated with r.i. spaces to be applied to problems in probability theory. On the other hand, probabilistic methods can also prove useful in the study of r.i. spaces. In this book new techniques are used and a number of interesting results are given, many of which have never before been available in English.