Compactness in the spaces of functions of bounded variation
Abstract
Recently the characterization of the compactness in the space BV([0,1]) of functions of bounded Jordan variation was given. Here, certain generalizations of this result are given for the spaces of functions of bounded Waterman -variation, Young -variation and integral variation. It appears that on the compact sets the norm is uniformly approximated by certain seminorms induced by the selection of finitely many intervals in [0,1].
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