Vol. 21, No. 3, 1967

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On Muirhead’s theorem

John Vincent Ryff

Vol. 21 (1967), No. 3, 567–576

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.

Mathematical Subject Classification
Primary: 26.70
Received: 11 November 1965
Revised: 14 April 1966
Published: 1 June 1967
John Vincent Ryff