The distribution of the values of a real almost periodic function or more generally of an almost periodic curve in several dimensions has been investigated lately by Wintner, Haviland and others.' One of the methods applied by Wintner depends on the use of Fourier transforms and is as such a standard method in the theory of probability. The object of the present paper is to point out that the established results can be deduced simply, and in a general form, from general theorems concerning Fourier transforms without introducing moment arguments.