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Lyapunov modular functions. (English) Zbl 1096.28005
The paper is related to the classical theorem of Lyapunov which says that an \(R^n\)-valued atomless \(\sigma\)-additive measure on a \(\sigma\)-algebra has a convex range. G. Knowles [SIAM J. Control 13, 294–303 (1974; Zbl 0302.49005)] generalized this theorem for non-injective measures with values in locally convex spaces. P. de Lucia and J. D. M. Wright [Rend. Circ. Mat. Palermo, II. Ser. 40, No. 3, 442–452 (1991; Zbl 0765.28011)] introduced the concept of convexity in topological groups and – with suitable modification of the definition of non-injectivity – transferred Knowles result to the case of group-valued measures. In the main result of the paper under review, this theorem of de Lucia and Wright is generalized for modular functions on complemented lattices.
Reviewer: Hans Weber (Udine)
MSC:
28B05 Vector-valued set functions, measures and integrals
06C15 Complemented lattices, orthocomplemented lattices and posets
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