Measure of a fuzzy set based on an arbitrary continuous t-conorms: the finite case

We suppose that a crisp decomposable measure is defined on a measurable space (R,A). Staring from this measure, we construct another decomposable measure on a suitable class of L-fuzzy subset of Ω, where L is a finite or countable subset of [0,1]. We don´t have any hypothesis about the structure of the two t-conorms which characterize the decomposition laws of the two measures, apart from the continuity one