Ch. I. Preliminaries. 1. Rearrangement invariant spaces. 2. The function of dilatation and Boyd indices. 3. Independent random variables. 4. Probability inequalities. 5. Disjoint random variables. 6. The Kruglov property. 7. Bases and sequence spaces. 8. Stable distributions -- Ch. II. Inequalities for sums of independent random variables in rearrangement invariant spaces. 1. Rosenthal's inequality and a characterization of the spaces L[subscript p]. 2. Estimates of von Bahr-Esseen type. 3. Upper estimates of the Rosenthal type. 4. Estimates in exponential Orlicz spaces -- Ch. III. Linear combinations of independent random variables in rearrangement invariant spaces. 1. l[subscript q]-estimates [actual symbol not reproducible]. 2. l[subscript 2]-estimates. 3. Stable random variables with different exponents. 4. Equidistributed random variables in exponential Orlicz spaces -- Ch. IV. Complementability of subspaces generated by independent random variables
Summary
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
Bibliography
Includes bibliographical references (pages 113-115) and index
