Compactness in the spaces of functions of bounded variation (Q6123778)

Summary: 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 \([0,1]\).