Compactness in the spaces of functions of bounded variation
Jacek Gulgowski · Zeitschrift für Analysis und ihre Anwendungen · 2024
Recently, the characterization of the compactness in the space \mathrm{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 \Lambda -variation, Young \Phi -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] .