The Lebesgue and Denjoy-Perron integrals from a descriptive point of view (Q1568170)

From the paper'' ``The conceptual affinity between the Denjoy-Perron and Lebesgue integrals was established vis-à-vis their Riemannian definitions of Henstock, Kurzweil and McShane more than twenty years ago. Nonetheless, the classical descriptive definitions of these integrals have little in common. Moreover, the \(\text{ACG}_*\) description of the indefinite Denjoy-Perron integral is cumbersome and relies completely on the order structure of the reals. Modifying the variational measures of Thomson and using a different technique than that employed by Bongiorno, Di Piazza, and Skvortsov, we elucidate the similarities between the contemporary descriptive definitions of the Lebesgue and Denjoy-Perron integrals''.