On the Farkas lemma and the Horn-Tarski measure-extension theorem. (English) Zbl 1317.15005
Summary: We 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.
MSC:
| 15A06 | Linear equations (linear algebraic aspects) |
| 28A60 | Measures on Boolean rings, measure algebras |
Keywords:
nonnegative solutions of systems of linear equations; Farkas lemma; measure extension; state on a Boolean algebra; Horn-Tarski criterionReferences:
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