Markov′s Theorem Revisited

Abstract

The fact that Markov′s Theorem holds for determinate measures is often overlooked and the theorem is stated for measures with compact support as did Markov. We give a brief survey of the history of the theorem as well as a proof in the determinate case. We also prove a version of Markov′s theorem in the indeterminate case. The results are applied to the shifted moment problem.