Statistical convergence and ideal convergence for sequences of functions

In this thesis, we discuss various kinds of statistical convergence and I-convergence for sequences of functions with values in ? or in a metric space. For real valued measurable functions defined on a measure space (X ,M,? ) , we obtain a statistical version of the Egorov theorem. We show that, in its assertion, equi-statistical convergence on a big set cannot be replaced by uniform statistical convergence. Also, we consider statistical convergence in measure and I-convergence in measure, with some consequences of the Riesz theorem. We prove that outer and inner statistical convergences in measure are equivalent if the measure is finite.