Statistical convergence of measurable functions

This study consists of five chapters. In the first chapter of this thesis, statistical convergence, measurements, and a brief history of statistical convergence of measurable functions are mentioned. In the second chapter, some definitions and theorems are given to be used in the thesis. In the third chapter, measures, measurement and integral theory, Lebesgue measurement, measurable functions, natural density, statistical convergence and their properties are given. Relationships between statistical convergence and Cesàro summability, some basic definitions and theorems that will be used in the next sections on statistical convergence sequences are given. In the fourth chapter, the concepts of statistical limit, lower limit and upper limit of a measurable function, statistical convergence in ∞ and some definitions and theorems are given. At the same time, strong Cesàro summability in ∞, statistical convergence of Fourier transforms, lower and upper statistical limits in ∞, Statistical limit in c∈ℝ, Statistical lower and upper limits in c∈ℝ, some definitions and theorems are given. In the fifth last chapter, the definitions of strong Cesàro summability and statistical convergence of Fourier integral, uniformly strong Cesàro summability locally, uniformly strong Cesàro additivity on ℝ and some theorems related to these definitions are given.