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

## TL;DR

The paper provides a simple proof linking a limit condition on a continuous local martingale to the expectation of an exponential involving the martingale and its quadratic variation, clarifying a result related to Girsanov's theorem.

## Contribution

It offers a straightforward proof of a specific limit condition implying an exponential expectation equality for continuous local martingales.

## Key findings

- Established a simple proof for the limit condition and exponential expectation equivalence.
- Clarified the relationship between the limit infimum condition and Girsanov's theorem.
- Contributed to the theoretical understanding of martingale exponential moments.

## Abstract

We give a simple proof that for a continuous local martingale $M_{t}$ $$ \liminf_{\varepsilon\downarrow0}\varepsilon \log Ee^{(1-\varepsilon) \langle M\rangle_{\infty}/2}<\infty \Longrightarrow E\exp(M_{\infty}-\langle M\rangle_{\infty}/2)=1. $$