Vol. 60, No. 1, 1975

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On the inequality i=1npif(pi) f(qi) 1

Pál Fischer

Vol. 60 (1975), No. 1, 65–74
Abstract

We show that the inequality

∑n   f(pi)-
pif(qi) ≧ 1,
i=1

for all P,Q An = {P ∈ Rn : P = (p1,p2,⋅⋅⋅,pn) where i=1npi = 1 and pi > 0 for i = 1,2,⋅⋅⋅,n} and some integer n 3, implies that f(p) = Apc 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
Authors
Pál Fischer