Some types of convergence and related Baire systems

Abstract

We study several kinds of convergence of sequences of real numbers with indices $\overline{m} \in N^n$ and the respective versions for uniform and pointwise convergence of sequences of real functions. We obtain a theorem about generalized Baire classes of real functions. This theorem is related to a result by Katetov from 1972. We add some comments and applications connected with ideal convergence, a generalization of statistical convergence investigated by several authors.