IDEAL EPI-CONVERGENCE OF SEQUENCES OF FUNCTIONS

Abstract

There are many definitions of epi-convergence in the literature. These definitions can be categorized as sequential, topological and epigraphical. In this paper, we will first give the epigraphical definition of ideal epi-convergence, and from this definition we will derive other definitions. In addition, we will see that the definition of epi-convergence can be given over the level sets. We will also answer the question of what is the relationship between ideal epi-convergence and ordinary epi-convergence.