Quasi sure version of a theorem of littlewood

Let (c _n) _nZ be a double-sided sequence of complex numbers; if, for quasi-all (i.e. in the Baire sense) choices of signs ( _n) _nZ , ( _n c _n) _nZ is a Fourier-Stieltjes sequence, then we prove that (c _n) _nZ l ² (Z); this extends a result of Littlewood and at the same time provides a very simple proof of this result.