Braverman M.S. Independent Random Variables and Rearrangement Invariant Spaces

Cambridge: Cambridge University Press, 1994. —124 p.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.Rearrangement invariant spaces
The function of dilatation and Boyd indices
Independent random variables
Probability inequalities
Disjoint random variables
The Kruglov property
Bases and sequence spaces
Stable distributions
Rosenthal's inequality and a characterization of the spaces LP
Estimates of von Bahr-Esseen type
Upper estimates of the Rosenthal type
Estimates in exponential Orlicz spaces
4-estimates (q# 2)
12-estimates
Stable random variables with different exponents
Equidistributed random variables in exponential Orlicz spaces
Subspaces generated by bounded random variables
Subspaces generated by equidistributed random variables