∆-uniform convergence and some limit theorems

In the introduction part of this thesis, the concept of time scale is reminded and information about the history of the subject is given. In the second part of this work, the concepts of semiring, measure built on semirings, external measure, external measure obtained by a measure, measurable set, Carathéodary extension of measure for time scale are studied. In the third chapter, by examining the subject of analysis on the time scale, we have included important definitions and theorems about the differentiation, integral, Riemann ∆-Integral on the time scale. In the fourth part of the thesis, the subject of measure theory on the time scale is explained. In the fifth chapter, we have obtained some results of ∆-uniform convergence by generalizing the point and uniform convergence of the sequences of functions in classical analysis to the ∆-point and ∆-uniform convergence of real valued function families defined on the time scale. In the last part, the properties of the concepts of ∆-point and-uniform convergence are investigated, and we have constructed the limit theorems related to Riemann ∆-integral of ∆-uniformly convergent function families.