On the points of regularity of multivariate functions of bounded variation
Points of non-regularity are studied for multivariate functions of bounded variation, denoted BV. Among numerous versions of the latter notion the author chooses to deal with that connected with the names of Vitali, Lebesgue, Fréchet, and de la Vallée Poussin which proved to be useful in the theory of measure and integration but less in the theory of trigonometric series, where the Hardy variation is more suitable. It is shown in the paper that BV functions vanishing at infinity are non-regular at most on a subset of \(\mathbb R^n\) Lebesgue measure zero, and the result is best possible.
scientific article; zbMATH DE number 2151933