On a Sufficient Condition for Absolute Continuity

摘要

The formulation of a condition which yields absolute continuity when combined with continuity and bounded variation is the problem considered in the paper. The formal statement of this condition, called interchangeable additivity of the second kind, as a definition is the purpose of the paper. Briefly, the formulation is achieved through a discussion which develops a proof by contradiction of a sufficiently theorem for absolute continuity which uses in its hypothesis the condition of continuity and bounded variation.