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Turkish Journal of Mathematics

Abstract

The theory of time scales was introduced by Stefan Hilger in his Ph. D. thesis in 1988, supervised by Bernd Auldbach, in order to unify continuous and discrete analysis [5]. Measure theory on time scales was first constructed by Guseinov [4], then further studies were made by Guseinov-Bohner [1], Cabada-Vivero [2] and Rzezuchowski [6]. In this article, we adapt the concept of Lebesgue-Stieltjes measure to time scales. We define Lebesgue-Stieltjes \Delta and \nabla-measures and by using these measures, we define an integral adapted to time scales, specifically Lebesgue-Stieltjes \Delta-integral. We also establish the relation between Lebesgue-Stieltjes measure and Lebesgue-Stieltjes \Delta-measure, consequently between Lebesgue-Stieltjes integral and Lebesgue-Stieltjes \Delta- integral.

DOI

10.3906/mat-0711-11

Keywords

Time scales, Lebesgue-Stieltjes \Delta-measure, Lebesgue-Stieltjes \Delta-integral.

First Page

27

Last Page

40

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Mathematics Commons

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