Doob built on work by Paul Lévy and, during the 1940's and 1950's, he developed basic martingale theory and many of its applications.
Doob nakapaloob sa trabaho sa pamamagitan ng Paul magpataw ng buwis at, sa panahon ng 1940's at 1950's, siya ay binuo basic matingeil teorya at marami ng kanyang aplikasyon.