Introduction

Abstract

There is a certain intuitive appeal to the vague notion that the 2 components of a vectorxare ``less spread out'' or ``more nearly equal'' 3 than are the components of a vectory. Not surprisingly, the notion 4 arises in a variety of contexts, and it can be made precise in a number 5 of ways. But in remarkably many cases, the appropriate precise state- 6 ment is that ``xis majorized byy'' (writtenx