On the inequality ∑ _i=1ⁿp_i ≧ 1

Pál Fischer

Vol. 60 (1975), No. 1, 65–74

DOI: 10.2140/pjm.1975.60.65

Abstract

We show that the inequality

for all P,Q ∈ A_n = where ∑ _i=1ⁿp_i = 1 and p_i > 0 for and some integer n ≧ 3, implies that f(p) = Ap^c where A is an arbitrary nonzero constant and either c ≦−1 or c ≧ 0. The converse holds as well, so that this result yields a characterization of the information gain.

Mathematical Subject Classification 2000

Primary: 94A15

Milestones

Received: 10 June 1974

Published: 1 September 1975