On the Farkas lemma and the Horn–Tarski measure-extension theorem

Abstract

MSC: 15A06 06E99 28A60 Keywords: Non-negative solutions of systems of linear equations The Farkas lemma Measure extension State on a Boolean algebra The Horn-Tarski criterionWe first derive a certain version of the Farkas lemma called the 0-1 Farkas lemma (the 0-1 FL). We then show that the 0-1 FL is equivalent to a measure-extension theorem. By applying one implication of this result, we prove that the 0-1 FL implies the classical Horn-Tarski measure-extension theorem.