Observables on perfect MV-algebras

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F19%3A73590161" target="_blank" >RIV/61989592:15310/19:73590161 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0165011418306894" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0165011418306894</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.fss.2018.11.018" target="_blank" >10.1016/j.fss.2018.11.018</a>

Result language
angličtina
Original language name
Observables on perfect MV-algebras
Original language description
An observable on an MV-algebra is any σ-homomorphism from the Borel σ-algebra B(R) into the MV-algebra which maps a sequence of disjoint Borel sets onto summable elements of the MV-algebra. We establish that there is a one-to-one correspondence between observables on Rad-Dedekind σ-complete perfect MV-algebras with principal radicals and their spectral resolutions. It means that we show that our partial information on an observable known only on all intervals of the form (−∞,t) is sufficient to determine the whole information about the observable. In addition, this correspondence allows us to define the Olson order which is a partial order on the set O(M) of all observables on an MV-algebra M as well as, we can define a sum of observables, so that O(M) becomes a lattice-ordered semigroup.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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