Topological properties of the range of mesures which are decomposable with respect to an abstract t-conorm are studied leading to the following Theorem: ”Let be a \(\perp\)-decomposable measure on (X,A), with respect to an Archimedian non-strict to-conorm \(\perp\), such that \(0<\mu (A)<1\), for every \(A\in {\mathcal A}-\{\phi,X\}\). If R(\(\mu)\) is infinite, then 1 is an accumulation point of R(\(\mu)\).”
A Lyapunov-like theorem for \(\perp\)-decomposable measures is also introduced like the following: ”Let (A,\({\mathcal A})\) be a measurable space and \(\mu\) a \(\perp\)-decomposable measure with respect to the Archimedian t-conorm И. If \(\mu\) is strongly continuous then \(R(\mu)=[0,1].''\)