CONTINUITY OF δ-VARIATION AND CONSTRUCTION OF CONTINUOUS MAJOR AND MINOR FUNCTIONS FOR THE PERRON INTEGRAL
Skvortsov · Real Analysis Exchange · 1995
It is proved that if a function is continuous on an interval, then its variations on a set taken relative to some covering relations are also continuous as interval-functions. This result is applied to a direct construction of continuous Perron major and minor functions of Henstock integrable function.