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A Helly theorem in the setting of Banach spaces. (English) Zbl 1006.28008
In the paper a Riemann-Stieltjes-type integral for real-valued functions with respect to Banach-space-valued maps is investigated. A Helly-Bray-type theorem for this type of integral is proved. Furthermore, some applications to the solution of the moment problem and to representation theorems for weakly compact linear Banach-space-valued operators, defined on the space of real-valued continuous functions, are given.
##### MSC:
 28B05 Vector-valued set functions, measures and integrals 47B07 Linear operators defined by compactness properties 52A35 Helly-type theorems and geometric transversal theory