The essential variation of a function and some convergence theorems
The paper contains the definition of the essential variation of a real function defined on a set \(E\) of real numbers. If \(E\) is a Lebesgue measurable set, then \(V(f,E) =\int_E|\overline Df(x)|dx\) for an arbitrary function \(f\). Also the passing to the limit under the sign of the Denjoy-Perron integral is studied.
scientific article; zbMATH DE number 913002