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Licensed Unlicensed Requires Authentication Published by De Gruyter July 19, 2019

On a Choquet-Stieltjes type integral on intervals

Sorin G. Gal
From the journal Mathematica Slovaca

Abstract

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.

MSC 2010: Primary 28A25; 26A42

  1. (Communicated by Anatolij Dvurečenskij)

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Received: 2018-12-02
Accepted: 2018-12-28
Published Online: 2019-07-19
Published in Print: 2019-08-27

© 2019 Mathematical Institute Slovak Academy of Sciences