A note on observables on MV-algebras

 A criterion when a subset of an MV-algebra is contained in the range of a (finitely additive) observable is given. It is used to prove that every at most countable subset of any MV-algebra is contained in the range of an observable. A much stronger result holds for any bold fuzzy algebra 0,1] ^S , which is whole contained in the range of a (σ-additive) observable.