Statistical convergence of multiple sequences

We extend the concept of and basic results on statistical convergence from ordinary (single) sequences to multiple sequences of (real or complex) numbers. As an application to Fourier analysis, we obtain the following Theorem 3: (i) If f is an element of L (log(+) L)(d-1) (T-d), where T-d := [-pi, pi)(d) is the d-dimensional torus, then the Fourier series of f is statistically convergent to f (t) at almost every t is an element of T-d; (ii) If f is an element of C(T-d), then the Fourier series of f is statistically convergent to f (t) uniformly on T-d.