Sliding window convergence and lacunary statistical convergence for measurable functions via modulus function

Abstract

In this paper we study the concepts of sliding window convergence for real valued measurable functions dened on [0,1) via modulus function. We also establish some inclusions and consistency theorems for sequential methods along with examples. Finally, we give a Cauchy convergence criterion.

Keywords

• modulus function
• sliding window method
• statistical convergence
• lacunary statistical convergence
• measurable functions
• Cauchy criteria