Integral Representation of Functions : New Proofs of Classical Results

In this paper we give new proofs of classical results wich establish that under certain hypotheses a function can be expressed almost everywhere as an indefinite repeated integral of its Riemann derivatives. These results were originally proved in the first half of the century and are fundamental in the theory of trigonometric series. They reveal their importance also in proving characterization of generalized convex functions. Recently a new proof of such kind of results has been given by M. Ash