A new proof for the conditions of Novikov and Kazamaki

We provide a novel proof for the sufficiency of certain well-known criteria that guarantee the true martingality of a continuous, positive local martingale. More precisely, we show that generalizations of Novikov’s condition and Kazamaki’s criterion follow directly from the existence of the Föllmer measure. The proof also yields a version of these criteria that guarantees the martingality of an only nonnegative, continuous local martingale.