On approximation of random integral means by integral means of partial sums of Fourier series (Q1896880)

The author proves two theorems on the approximation of the integral mean of a periodic function in several variables by the integral mean of the rectangular partial sum of its multiple Fourier series. One of the theorems is formulated in terms of expectation, while the other in terms of convergence to zero in probability. The paper ends with two appendices containing a brief computer program written in PASCAL and a table which exhibits the efficiency of the approximation procedure.