English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

We show that under some natural conditions, we are able to lift an$n$-dimensional spectral resolution from one monotone $\sigma$-complete unitalpo-group into another one, when the first one is a $\sigma$-homomorphic imageof the second one. We note that an $n$-dimensional spectral resolution is amapping from $\mathbb R^n$ into a quantum structure which is monotone,left-continuous with non-negative increments and which is going to $0$ if onevariable goes to $-\infty$ and it goes to $1$ if all variables go to $+\infty$.Applying this result to some important classes of effect algebras includingalso MV-algebras, we show that there is a one-to-one correspondence between$n$-dimensional spectral resolutions and $n$-dimensional observables on theseeffect algebras which are a kind of $\sigma$-homomorphisms from the Borel$\sigma$-algebra of $\mathbb R^n$ into the quantum structure. An important usedtool are two forms of the Loomis--Sikorski theorem which use two kinds oftribes of fuzzy sets. In addition, we show that we can define three differentkinds of $n$-dimensional joint observables of $n$ one-dimensional observables.

Lifting, $n$-Dimensional Spectral Resolutions, and $n$-Dimensional Observables