Asymptotic double subseries

Abstract

In 1964 Salat presented a notion of asymptotic density of single dimensional subseries. Using this notion he presented a series of theorems similar to the following. If dn be a decreasing sequence such that lim infn ndn > 0 and let the subseries (x) = ?? k=1 ?k(x)dk of the series ?? k=1 dk be convergent, then p(x) = limn p(n,x)/n=0. Following Salat?s patten, we present a notion of double subseries and a natural variation of Salat?s theorem.