Fuzzy equality and convergences for F-observables in F-quantum spaces
The paper deals with F-states (P-measures) and F-observables on F-quantum spaces (soft fuzzy \(\sigma\)-algebras). Fuzzy equalities and fuzzy inequalities are defined for fuzzy sets, F-observables and the corresponding notions in the representation of \textit{A. Dvurečenskij} [On a representation of observables in fuzzy measurable spaces, to appear in J. Math. Anal. Appl.]. The authors introduce 14 types of convergence of F-observables. These appear to be equivalent to the corresponding types of convergence of measurable functions on a Boolean \(\sigma\)- algebra used in the representation. Using this fact, a series of implications between various types of convergence is proved.
P-measures) and F-observables on F- quantum spaces
scientific article; zbMATH DE number 4210475