Applications of deferred Lebesgue product measurable convergence to approximation theorems

Abstract

In this paper, we introduce the notions of product measurable convergence, deferred Cesàro statistical product measurable convergence and deferred Cesàro statistical Lebesgue product measurable convergence for sequences of measurable functions on product measure spaces. We establish some fundamental relations among these convergences and also give several explanatory examples in support of our definitions and results. Finally, as an application, we prove a new version of Korovkin-type approximation theorems for sequences of measurable functions on product measure spaces by using the notion of deferred Cesàro statistical Lebesgue product measurable convergence.