N where SN= ~ c ~ and S_1=0. r t ~ 0 We shall denote by U, S and A the classes of functions fbelonging to C whose Fourier series converge uniformly, strongly uniformly and absolutely on [0, 2~], respectively. Tanovic--Miller showed that the set A is a real subset o f S which itself is a real subset of U ([2], Theorem 4). By the Fej6r theorem we can see that if fE U then f i s the sum of its Fourier series and in the cases f E S or fEA a similar conclusion is valid. Of course, if f is a sum of uniformly, strongly uniformly or absolutely convergent trigonometric series then fEU, f E S or fEA, respectively. To show the difference between the uniform and strong uniform convergence we have the following trivial