RIEČAN AND BOSBACH STATES ON GLIVENKO RESIDUATED LATTICES

Bosbach and Riečan states on residuated lattices both are analogues of probability measures on Boolean algebras. In this paper it is proved that Riečan states on a residuated lattice is uniquely determined by its restriction on the subset of all regular elements and consequently the same holds for Bosbach states on Glivenko residuated lattices. These results indicate that for studies of Riečan and Bosbach states one can concentrate only on involutive residuated lattices.