On the harmonic averages of numerical sequences

In recent years, the almost sure central limit theorem attracted widespread attention in Probability Theory. It involves the harmonic (also called logarithmic) averages of a certain numerical sequence formed from a sequence of independent, identically distributed random variables. Our primary aim is to study the convergence behavior of the sequence of harmonic averages of a given numerical sequence from the viewpoint of Summability Theory. Received: 12 May 2005; revised: 1 July 2005