The theorem of averaging for the almost-periodic functions

It is proved that the limit of maximal mean is an independent variable of initial conditions if a vector exists from the convex hull of a compact set out of a finite-dimensional space and the components of vector are independent variables with respect to the spectrum of almost-periodic function. The compact set is the right hand of differential inclusion. The limit of maximal mean is taken over all solutions of the Couchy problem for the differential inclusion.