A discrete Korovkin theorem

Abstract

In this paper we give a sufficient condition for the pointwise Korovkin property on B( X), the space of bounded real valued functions on an arbitrary countable set X = { x l ,…, x j ,…}. Our theorem follows from its L p ( X, μ) analogue (and conversely); here 1 ⩽ p < ∞ and μ is a positive finite measure on X such that μ({ x j }) > 0 for all j.