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Nonatomic vector-valued modular functions. (English) Zbl 0987.28012
Let \(\mu:{\mathfrak F}\to X\) be a \(\sigma\)-additive Banach space valued measure of bounded variation on a \(\sigma\)-algebra. By results of J. J. Uhl jun. [Proc. Am. Math. Soc. 23, 158-163 (1969; Zbl 0182.46903)] and 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.
Reviewer: Hans Weber (Udine)

28B05 Vector-valued set functions, measures and integrals
06C15 Complemented lattices, orthocomplemented lattices and posets
46G10 Vector-valued measures and integration