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Statistical convergence and ideal convergence for sequences of functions. (English) Zbl 1119.40002

The paper discusses various types of statistical convergence and ideal convergence for sequences of functions with real values or with values in a more general metric space. The authors present very thoroughly the definitions and types of ideal convergence for functions and prove several results regarding ideal pointwise and ideal uniform convergence. The results are exemplified through analytical instances.

The main outcomes of the paper are the derivation and proof of two theorems, counterparts of the Egorov and Riesz theorems from classical analysis, in which statistical convergence of measurable functions is used.


MSC:
40A30Convergence and divergence of series and sequences of functions