Independent Random Variables and Rearrangement Invariant Spaces [Paperback]

Professor Braverman investigates independent random variables in rearrangement invariant (r.i.) spaces.The subject lies on the boundary between probability theory and the theory of function spaces in this investigation of independent random variables in rearrangement invariant (r.i.) spaces. New techniques are used and a number of interesting results are given.The subject lies on the boundary between probability theory and the theory of function spaces in this investigation of independent random variables in rearrangement invariant (r.i.) spaces. New techniques are used and a number of interesting results are given.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.1. Preliminaries; 2. Inequalities for sums of independent random variables in rearrangement invariant spaces; 3. Linear combinations of independent random variables in rearrangement invariant spaces; 4. Complementibility of subspaces generated in rearrangement invariant spaces; 5. Independent random variables in rerrangement invariant spaces.