On some variational measures related to the wide Denjoy integral and its counterparts (Q2177973)

In this article, the author establishes the coincidence of two types of variational measures (called weak, respectively \(q\)-weak) introduced in [\textit{B. S. Thomson}, Real Anal. Exch. 41, No. 1, 173--226 (2016; Zbl 1387.26009)] with the variational measures coming from Riemann definitions of wide Denjoy integrals. Applications are given to characterize various Lusin-type integrals defined using the notions of generalized absolute continuity (ACG) and generalized bounded variation (BVG) via absolute continuity of these measures. The paper continues the previous work [Rend. Semin. Mat. Univ. Padova 126, 175--200 (2011; Zbl 1232.26007)] of the author.