  In this paper we follow a paper from A. Sedunova (2017) regarding R. C.
Vaughan's basic mean value Theorem (Acta Arith. 1980) to improve and complete a
more general demonstration for a suitable class of arithmetic functions as
started by A. C. Cojocaru and M. R. Murty (London Math. Soc. Stud. Texts 2006).
As an application we derive a basic mean value Theorem for the von Mangoldt
generalized functions.
