A note on Rado's theorem

In this note, a theorem of Rado which characterizes the convex hull of the set of all rearrangements of a given real n-tuple in terms of the Hardy—Littlewood—Pólya spectral order relation < is shown to be a consequence of a result of Hardy—Littlewood—Pólya and a strong spectral inequality.Subject classification (Amer. Math. Soc. (MOS) 1970): 52 A 40, 52 A 20.