On approximate strong and approximate uniform differentiability

Abstract

In this paper we introduce the definitions of approximate strong and approximate uniform differentiability and prove that a function having finite approximate derivative on an interval I is applied approximately uniformly diiferentiable at a point if and only if it is approximately strongly differentiable there. We also introduce the definition of essentially AC [BVl functions and prove that a measurable EVG function on a set wilh finite measure is essentially AG.