Supplement to ``Weak domination principle''

Abstract

Lemma 4 in the previous paper "weak domination principle" in the volume 28 of this journal is true without the assumption on non-degeneracy. Namely, if G is a positive kernel on Ω = {xu x2, X3} satisfying the weak domination principle, then it satisfies the ordinary domination principle or the inverse domination principle. To see this, let 7Ί2 = 0. Since ϊ23 = 0 implies 7*31 = 0, it is sufficient to notice the imcompatibility of ϊ23 > 0 and Tsi < 0. Thus the main theorems in the paper are to be stated without assuming non-degeneracy as follows.