Browsing by Author "Deniz, Ash"

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    Lebesgue-Stieltjes Measure on Time Scales
    (Scientific Technical Research Council Turkey-Tubitak, 2009) Deniz, Ash; Ufuktepe, Ünal
    The theory of time scales was introduced by Stefan Hilger in his Ph. D. thesis in 1988, supervised Bernd Auldbach, in order to unify continuous and discrete analysis [5]. Measure theory oil 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 del-measures and by using these measures, we define ail 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.