We found a match
Your institution may have rights to this item. Sign in to continue.
- Title
A NOTE ON FIELD-VALUED MEASURES.
- Authors
DE SIMONE, ANNA; HROCH, MICHAL; PTÁK, PAVEL
- Abstract
We consider the Horn-Tarski condition for the extension of (signed) measures (resp., non-negative measures) in the setup of field-valued assignments. For a finite collection 𝓒 of subsets of Ω, we find that the extension from 𝓒 over the collection exp Ω of all subsets of Ω is implied by, and indeed equivalent to, a certain type of Frobenius theorem (resp. a certain type of Farkas lemma). This links classical notions of linear algebra with a generalized version of Horn-Tarski condition on extensions of measures. We also observe that for a general (infinite) 𝓒 the Horn-Tarski condition guarantees the extension of signed measures (here the standard Zorn lemma applies). However, we find out that the extensions for non-negative ordered-field-valued measures are generally not available.
- Subjects
LINEAR algebra; FROBENIUS algebras; MATHEMATICS theorems; SUBSET selection; QUANTUM logic
- Publication
Mathematica Slovaca, 2017, Vol 67, Issue 6, p1295
- ISSN
0139-9918
- Publication type
Article
- DOI
10.1515/ms-2017-0052