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Helly’s selection principle for functions of bounded \(p\)-variation. (English) Zbl 1092.26003

Summary: The classical Helly’s selection principle states that a uniformly bounded sequence of functions with uniform bounded variation admits a subsequence which converges pointwise to a function of bounded variation. Helly’s selection principle for metric space-valued functions of bounded \(p\)-variation is proven answering a question of Chistyakov and Galkin.

MSC:

26A45 Functions of bounded variation, generalizations
40A30 Convergence and divergence of series and sequences of functions
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