A SIMPLE PROOF OF DOOB'S CONVERGENCE THEOREM

Doob's version of the fundamental convergence theorem of potential theory asserts that if (f_n) is a decreasing sequence of excessive functions and f is the supermedian function inf f_n, then the set where f differs from (its regularized function) is semi-polar. Many beautiful proofs of this result are available in the literature. Here is a trivial one…