Korovkin’s theorem is an abstract result in approximation theory which givesconditions for uniform approximation of continuous functions on a compact metricspace using sequences of positive linear operators (on the space of continuous functions). It gives simple proofs of major approximation theorems in analysis like the Weierstrass approximation theorem and Fejer’s theorem on the Cesaro summability of Fourier series. A measure theoretic version of Korovkin’s theorem, which seems to be new, will be stated and proved. It will also be shown how the theorems mentioned above can be deduced from this.