Strong law of large numbers for positively and negatively dependent random fields indexed by sets (Q1866858)

The author establishes sufficient conditions for the strong law of large numbers to be satisfied for random fields on \(\mathbb N^d\), \(d\geq 1\), consisting of mutually positively or negatively dependent values. An almost sure uniform convergence of partial sums is studied, the sums being indexed by the elements of a system of the Lebesgue subsets \([0,1]^d\). The optimality of the proposed conditions is shown.