Characterizations of functions of bounded variation on effect algebras

Abstract

In this paper, the concept of [Formula: see text]-null-additivity on effect algebras is introduced and investigated. Theorems connecting null-additivity and [Formula: see text]-null-additivity are also proved. Further, pseudo-metric generating property is studied and its relation with null–null-additivity is also explored. Some theorems are also obtained as characterizations for functions of bounded variation on effect algebras. Finally, it is shown that limit of every monotone sequence exists for a function of bounded variation defined on effect algebras even if the function is not continuous from above and (or) below.