A Necessary and Sufficient condition that should be comparable with for all Positive values of the is that one of () and () should be majorized by the other. If , then

with equality only when () and () are identical or when all the are equal. See Hardy et al. (1988) for a definition of notation.

References

Hardy, G. H.; Littlewood, J. E.; and Pólya, G. Inequalities, 2nd ed. Cambridge, England: Cambridge University Press, pp. 44-48, 1988.