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.
