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The sum of two Radon-Nikodym-sets need not be a Radon-Nikodym-set. (English) Zbl 0593.46021
It is shown in the present note that there are closed, convex, bounded Radon-Nikodym-sets \(C_ 1\) and \(C_ 2\) such that \(C_ 1+C_ 2\) is closed but not a Radon-Nikodym-set, as it contains a copy of the unit- ball of \(c_ 0\).

MSC:
46B22 Radon-Nikodým, Kreĭn-Milman and related properties
46G10 Vector-valued measures and integration
46B20 Geometry and structure of normed linear spaces
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