Article
Keywords:
$F$-quantum space; $F$-state; $F$-observable; representation theorem of $F$-observables; convergence of $F$-observables; soft fuzzy $\sigma$-algebras; fuzzy equalities; fuzzy inequalities; fuzzy sets
Summary:
We introduce a fuzzy equality for $F$-observables on an $F$-quantum space which enables us to characterize different kinds of convergences, and to represent them by pointwise functions on an appropriate measurable space.
References:
[1] S. P. Gudder H. C. Mullikin:
Measure theoretic convergences of observables and operators. Journal of Mathematical Physics, 14 (1973), 234-242.
DOI 10.1063/1.1666301 |
MR 0334747
[2] B. Riečan: A new approach to some notions of statistical quantum mechanics. Busefal, 35, (1988), 4-6.
[3] A. Dvurečenskij:
On existence of probability measures on fuzzy measurable spaces. (to appear in Fuzzy Sets and Systems).
MR 1128000
[5] A. Dvurečenskij A. Tirpáková: A note on a sum of observables in F-quantum spaces and its applications. Busefal, 35 (1988), 132-137.
[6] K. Piasecki:
On fuzzy F-measures. In: Proc. First Winter School on Measure Theory, Liptovský Ján, Jan. 10-15, 1988, 108-112.
MR 1000200
[7] A. Dvurečenskij:
On a representation of observables in fuzzy measurable spaces. (to appear in J. Math. Anal. Appl.).
MR 1372199
[8] A. Dvurečenskij B. Riečan:
On joint distribution of observables for F-quantum spaces. (to appear in Fuzzy Sets and Systems).
MR 1089012
[9] T. Neubrunn B. Riečan:
Measure and Integral. (Slovak). VEDA Bratislava 1981.
MR 0657765