Deniz, AslıUfuktepe, Ünal2017-01-032017-01-032009Deniz, A., and Ufuktepe, Ü. (2009). Lebesgue-Stieltjes measure on time scales. Turkish Journal of Mathematics, 33(1), 27-40. doi:10.3906/mat-0711-111300-00981303-61491300-0098http://dx.doi.org/10.3906/mat-0711-11https://hdl.handle.net/11147/2703https://search.trdizin.gov.tr/yayin/detay/89349The 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 Δ and ▶-measures and by using these measures, we define an integral adapted to time scales, specifically Lebesgue-Stieltjes Δ-integral. We also establish the relation between Lebesgue-Stieltjes measure and Lebesgue-Stieltjes Δ-measure, consequently between Lebesgue-Stieltjes integral and Lebesgue-Stieltjes Δ-integral.eninfo:eu-repo/semantics/openAccessLebesgue-Stieltjes Δ-integralLebesgue-Stieltjes Δ-measureTime scalesArticle2-s2.0-6234911802610.3906/mat-0711-11