Abstract:Motivated by the limitations of the traditional definitions of the Riemann-Stieltjes and Darboux-Stieltjes integrals, we introduce a generalized Darboux-Stieltjes integral that is equivalent to an earlier generalization by Ross [19]. Our definition builds upon an approach to the Darboux-Stieltjes integral recently introduced by the first author and Convertito [5]. We show that our definition agrees with all previous definitions, but that the class of integrable functions is much larger. We develop all the anal… Show more
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