Some properties of non-Newtonian Lebesgue measure in real numbers

This thesis consists of four chapters. In the first chapter, the information about the studies that are done until today and these application areas, were briefly given. In the second chapter, basic definitions and theorems about the thesis subject were given. In the third chapter, non-Newtonian open and closed sets were defined and basic theorems were given. In addition, the measure of non-Newtonian open set was given. The fourth chapter of the thesis is composed of three sections. In the first section, the measure of the bounded, closed set which is non-Newtonian is defined and basic theorems are given. In the second section, the inner and outher measures of the non-Newtonian bounded sets were defined and related theorems were given. In the last section, the measure of the non-Newtonian bounded sets in the sense of Lebesgue was defined and theorems were given.