A simple proof of a result of A. Novikov

We give simple proofs that for a continuous local martingale M_t:

1. \liminf_{\epsilon->0} \epsilon \log Ee^{(1-\epsilon) <M>\infty /2} < \infty ==> E\exp(M\infty - <M>\infty /2) = 1, 2) \liminf{\epsilon->0} \epsilon \log\sup_{t>=0} Ee^{(1-\epsilon)M_t/2} < \infty ==> E\exp(M_\infty - <M>_\infty /2) = 1 .