KRONECKER’S LEMMA AND A CONVERSE WITH APPLICATIONS

Abstract

 Kronecker’s Lemma asserts that the mean of a real sequence {a_n} is zero if  converges. We give a new proof for the case a_n ≥ 0. If {a_n} is bounded, a partial converse was given by Hlawka et al [5]. We state sevaral applications of this converse from our work.