Summary: Let \(\mathcal F\) be an algebra of real-valued bounded functions on \(\mathbb N\) which separates the points, which contains the constants and which is complete in the sup-norm. If \(L\) is a positive linear functional on \(\mathcal F\), then, for each \(f \in \mathcal F\), \(L(f)\) can be represented as an integral of \(\bar f\) on \(\beta \mathbb N\) where \(\bar f\) is the unique extension of \(f\) to the Stone-Čech compactification \(\beta \mathbb N\) of \(\mathbb N\).