A few comments on a result of A. Novikov and Girsanov's theorem

We give a simple proof that for a continuous local martingale $M_t$ $$\underset{\epsilon \downarrow 0}{\mathrm{lim\hspace{0.17em}inf}}\epsilon \log E{e}^{(1-\epsilon )⟨M{⟩}_{\mathrm{\infty }}\mathrm{/}2}<\mathrm{\infty }⟹E\exp (M_{\mathrm{\infty }}-⟨M{⟩}_{\mathrm{\infty }}\mathrm{/}2)=1.$$