ON A SPACE OF μ-STATISTICAL CONTINUOUS FUNCTIONS

Abstract

The concepts of mu-statistical discontinuities of the first and second kinds for functions in some measurable space with the measure mu are introduced in this work. The space of mu-statistical continuous functions on some interval is considered, some properties of functions in this space are studied. The relationship between this space and the spaces of continuous and Lebesgue-summable functions in the case where mu is a Lebesgue measure is also considered.