A DANIELL-STONE APPROACH TO THE GENERAL DENJOY INTEGRAL

In this note we shall introduce a, as far as we know, new kind of derivative (diagonal derivative), characterizing a certain class of functions E(d) and a generalized Daniell integral I(d) on this class. We follow Leinert and Konig to obtain a class of integrable functions L(d)1 belonging to E(d), using the method of Daniell-Stone integration without the lattice condition as described in [1] or similarly in [3]. Our main purpose is to show that we obtain exactly the Denjoy integrable functions.