Rearrangement Invariant Norms of Symmetric Sequence Norms of Independent Sequences of Random Variables
Abstract
Let X1, X2,..., Xn be a sequence of independent random variables, let M be a rearrangement invariant space on the underlying probability space, and let N be a symmetric sequence space. This paper gives an approximate formula for the quantity || ||(Xi)||N ||M whenever Lq embeds into M for some 1 le q < infty. This extends work of Johnson and Schechtman who tackled the case when N = lp, and recent work of Gordon, Litvak, Schuett and Werner who obtained similar results for Orlicz spaces.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.