Nonatomic vector-valued modular functions (Q2733900)

Let \(\mu:{\mathfrak F}\to X\) be a \(\sigma\)-additive Banach space valued measure of bounded variation on a \(\sigma\)-algebra. By results of \textit{J. J. Uhl jun.} [Proc. Am. Math. Soc. 23, 158-163 (1969; Zbl 0182.46903)] and \textit{V. M. Kadets} [Funct. Anal. Appl. 25, No. 4, 295-297 (1991; Zbl 0762.46031)] the range of \(\mu\) is relatively compact if \(X\) has the Radon-Nikodým property, and \(\overline{\mu({\mathfrak F})}\) is convex if \(\mu\) is atomless and \(X\) has the Radon-Nikodým property or is \(B\)-convex. In the paper under review, these theorems are generalized to modular functions on complemented lattices.