Several of the interesting
analytic and geometric conditions known to be equivalent to the classical partial
order ≺ on En given by Hardy, Littlewood and Pólya have also been shown to be
true in the continuous case. Muirhead’s inequality, from which virtually all
generalizations of the arithmetic-geometricmean inequality follow, is perhaps less
tractable and does not readily suggest a continuous analogue. The purpose of this
paper is to discuss two such possibilities.
The author is indebted to Professor G.-C. Rota who suggested that such a
generalization should exist.
