  Let h be a real-analytic function in the neighborhood of some compact set K
on the plane. We show that for any complex measure on the Euclidean space of a
finite total variation without singular components with the Fourier--Stieltjes
transform f(y) there exists another measure of a finite total variation with
the Fourier transform g(y) with the property g(y)=h(f(y)) for each y such that
f(y) belongs to K.
