A discrete Korovkin theorem (Q1061965)

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 \(X=\{x_ 1,...,x_ j,...\}\). Our theorem follows from its \(L_ p(X,\mu)\) analogue (and conversely); here \(1\leq p<\infty\) and \(\mu\) is a positive finite measure on X such that \(\mu (\{x_ j\})>0\) for all j.