  The article is devoted to the formulation and proof of the theorem on
convergence with probability 1 of expansion of iterated Ito stochastic
integrals of arbitrary multiplicity based on generalized multiple Fourier
series converging in the sense of norm in Hilbert space. The cases of multiple
Fourier-Legendre series and multiple trigonomertic Fourier series are
considered in detail. The proof of the mentioned theorem is based on the
general properties of multiple Fourier series as well as on the estimate for
the fourth moment of approximation error in the method of expansion of iterated
Ito stochastic integrals based on generalized multiple Fourier series.
