Linear Differential Equations with Fast and Slow Time

We shall assume that the elements aij(t, s) of the matrix A(t, s) are defined for −∞ < t, s < ∞, are almost periodic in the variable t uniformly with respect to s and almost periodic in s uniformly with respect to t. Then there exists the mean value of the matrix A(t, s) over the first variable

lim T→∞

1 T

T∫

A(t, s)dt = A¯(s).