Let al, ⃛ anbe distinct real numbers mod 2φ and letKbe a closed subset of [0, 1]. Define Ω to be the unit diskDfrom which the slitseiaK, j = 1 …nhave been removed, and letube the harmonic measure of∂Drelative to Ωet letrbe the corresponding harmonic measure when the a, are changed toIn case Ω is simply connected Dubinin has proved thatIn caseBaernstein has proved the stronger result that lor every increasing convex functionand everywe have the integral mean inequality