Group-valued measures on coarse-grained quantum logics

Simone, Anna De; Pták, Pavel

doi:10.1007/s10587-007-0110-4

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“…In extending states on a certain kind of quantum logics (see [2][3][4]; for some other related consideration, see also [8,10]), the results obtained are based on the (state) Horn-Tarski measure extension theorem (see [1], [3] and [9]). Let us call this theorem the HT proper.…”

Section: Introduction and Resultsmentioning

confidence: 99%

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

Simone

Pták

2015

Linear Algebra and its Applications

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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.

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Section: Introduction and Resultsmentioning

confidence: 99%

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

Simone

Pták

2015

Linear Algebra and its Applications

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“…An analogous problem has been studied in discrete setup in [3,4,7] and [11] (the extensions being found available). The "continuous" version pursued here has been initiated in [7].…”

Section: Introductionmentioning

confidence: 99%