Multidimensional sliding window pringsheim convergence for measurable functions

Abstract

Connor and Savas (Acta Math Hung 145:416-432, 2015) presented the concept of sliding window method. The main purpose of this article is to extend Connor and Savas results to higher dimension. To accomplish this we define a new summability method for multidimensional measurable real valued functions defined on [0,infinity)x[0,infinity). Additionally, we present a series of inclusion and consistency theorems and some examples.