Range of finitely additive fuzzy measures (Q1277872)

The authors present several results about the range of vector-valued (finitely additive) fuzzy measures \(\mu:{\mathcal A}\to E\) generalizing (essentially) known results for measures on Boolean algebras. Typical results are: The closure of \(\mu({\mathcal A})\) is convex if \(E\) is a \(B\)-convex Banach space, \({\mathcal A}\) has the interpolation property (a condition weaker than \(\sigma\)-completeness) and \(\mu\) is nonatomic and of bounded variation. \(\mu({\mathcal A})\) is convex if \(E\) is finite dimensional, \({\mathcal A}\) has the interpolation property and \(\mu\) is nonatomic and bounded.