ИСТИНА

We prove that if a series with respect to the system of characters of a compact zero-dimensional group G (non-abelian case is also possible) is everywhere convergent to a finite function f then f is integrable on G in the sense of some generalization of Henstock integral and this series is the Fourier series of f. Some extensions to the non-abelian case of results of related to the properties of the sets of uniqueness are also obtained.