Institution: | a Institute of Mathematics, Technical University of ?ód?, ul. Wólczańska 215, 93-005 ?ód?, Poland b Center of Mathematics and Physics, Technical University of ?ód?, al. Politechniki 11, 90-924 ?ód?, Poland c Faculty of Mathematics, University of ?ód?, ul. Banacha 22, 90-238 ?ód?, Poland |
Abstract: | Let I⊂P(N) stand for an ideal containing finite sets. We discuss various kinds of statistical convergence and I-convergence for sequences of functions with values in R or in a metric space. For real valued measurable functions defined on a measure space (X,M,μ), we obtain a statistical version of the Egorov theorem (when μ(X)<∞). 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 (for sequences of measurable functions) are equivalent if the measure is finite. |