TANGENT SEQUENCES IN ORLICZ AND REARRANGEMENT-INVARIANT SPACES

Let (f(n)) and (g(n)) be two sequences of random variables adapted to an increasing sequence of sigma-algebras (F-n) such that the condition al distributions of f(n) and g(n) given F-n coincide. Suppose further that the sequence (g(n)) is conditionally independent. Then it is know n that \\Sigma f(k)\\(p) less than or equal to C\\Sigma g(k)\\(p), 1 l ess than or equal to p less than or equal to infinity, where the numbe r C is a universal constant. The aim of this paper is to extend. this result to certain classes of Orlicz and rearrangement invariant spaces . This paper includes fairly general techniques for obtaining rearrang ement invariant inequalities from Orlicz norm inequalities.