Sulla convergenza in categoria delle serie trigonometriche

Being evident (prop. 1) that the Fourier series of a function can be not convergent in cathegory (as defined in [4]) to the function itself, it is proved (Theorem 1) that for a continuous function f there exist a trigonometric series having partial sums uniformily bounded and converging to f on a set X of second category. It is also proved (prop. 2) that, even renouncing to the uniform boundedness of partial sums, the set X cannot be chosen of full measure.