Abstract

In this paper we extend the notion of equal convergence of Császár and Laczkovich with the help of ideals of the set of positive integers and introduce the ideas of $\Cal{I}$ and $\Cal{I}^*$-equal convergence and prove certain properties. Throughout the investigation two classes of ideals, one satisfying ``Chain Condition'' and another called $P$-ideals play a very important role. We also introduce certain related notions of convergence and prove an Egoroff-type theorem for $\Cal{I}^*$-equal convergence.

Keywords: Ideal; filter; $\Cal{I}$ and $\Cal{I}^*$-equal convergence; $P$-ideal; Chain condition; $\Cal{I}^*$-uniform equal convergence; $\Cal{I}^*$-almost uniform equal convergence; $\Cal{I}^*$-quasi vanishing restriction; Egoroff Theorem.

MSC: 40G15, 40A99, 46A99

Pages:  165$-$177     

Volume  66 ,  Issue  2 ,  2014