PROBABILISTIC PROOF OF THE MEAN-VALUE THEOREM FOR [0, 1]-VALUED MULTIPLICATIVE FUNCTIONS BY MEANS OF THE ADELIC FORMULATION

Abstract

A probabilistic proof by means of the adelic formulation is given to the classical mean-value theorem for [0, 1]-valued multiplicative arithmetical functions f. Then a more general mean-value theorem is derived for composite functions φ(f) of f with (semi-)continuous functions φ.