Statistical convergence of multiple sequences (Q1423763)

In this paper the notion of statistical convergence is generalized from ordinary sequences to double and multiple sequences of real or complex numbers. It is shown in analogy to the ordinary case that statistical convergence is equivalent to a statistical Cauchy property and that a statistical convergent sequence can be split into a convergent sequence and a sequence which vanishes on a set of density one. Furthermore the relation to strong Cesàro summability is considered and as application statistical convergence of Fourier series for functions \(f \in L(\log^+L)^{d-1}([-\pi,\,\pi]^d)\) is investigated.