On metrization of the space Dα[0, ∞)

Abstract

A complete metric on the function space D_α[0, ∞) , which is a subspace of the space D_α[0, ∞) of functions without discontinuities of the second kind, is constructed. This metric converts D_α[0, ∞) into a complete separable metric space. It is a modification of a metric on D_α[0, 1) introduced by Woodroofe, and is stronger than the well-known metrics on D_α[0, ∞). Conditions for compactmess of the subsets of D_α[0, ∞) are given.