ON FINITE CONVERGENCE INDEX

Abstract

Chaatit, Mascioni, and Rosenthal defined the class of functions of finite Baire index and proved that the class forms an algebra and a lattice. Following that idea, in this paper we define ¹((fn)), the finite convergence index of a given sequence of real-valued functions (fn). Let (fn); (gn) be sequences of real-valued functions on a Polish space X and (hn) be any of the sequences (fn)+(gn), (fn):(gn), maxf(fn); (gn)g, minf(fn); (gn)g, then we prove that ¹((hn)) · ¹((fn)) + ¹((gn)).

Key words and Phrases: finite convergence index, sequences of functions