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Optimal bundles in normed spaces. (English) Zbl 1263.41021

Summary: We prove the existence of optimal bundles for a countable set of data in a broad class of normed spaces, which extend previous known results for a finite data set in a Hilbert space. In addition, we study the behavior of deviations and diameters for an increasing sequence of data sets.

MSC:

41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
41A28 Simultaneous approximation