On an averaging process for functions of bounded variation (Q1821216)

The author considers the averaging process (in the sense of \textit{M. Laczkovich} and \textit{G. Petruska} [Acta Math. Acad. Sci. Hung. 39, 279- 287 (1982; Zbl 0451.26005)]) concerning the class V of functions of bounded variation, the class U of step functions and the class W of functions possessing both one-sided limits at every point, defined on \([0,1].\) He proves that W is the class of all average functions for each of the classes U, V and W.