On a Choquet-Stieltjes type integral on intervals

Year, pages: 2019, 801 - 814

In this paper we introduce a new concept of Choquet-Stieltjes integral of $f$ with respect to $g$ on intervals, as a limit of Choquet integrals with respect to a capacity $μ$. For $g(t)=t$, one reduces to the usual Choquet integral and unlike the old known concept of Choquet-Stieltjes integral, for $μ$ the Lebesgue measure, one reduces to the usual Riemann-Stieltjes integral. In the case of distorted Lebesgue measures, several properties of this new integral are obtained. As an application, the concept of Choquet line integral of second kind is introduced and some of its properties are obtained.

Gal, S. 2019. On a Choquet-Stieltjes type integral on intervals. In Mathematica Slovaca, vol. 69, no.4, pp. 801-814. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0269

Gal, S. (2019). On a Choquet-Stieltjes type integral on intervals. Mathematica Slovaca, 69(4), 801-814. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0269

Publisher: Mathematical Institute, Slovak Academy of Sciences, Bratislava