Local martingales in discrete time

For any discrete-time P–local martingale S there exists a probability measure Q∼P such that S is a Q–martingale. A new proof for this result is provided. The core idea relies on an appropriate modification of an argument by Chris Rogers, used to prove a version of the fundamental theorem of asset pricing in discrete time. This proof also yields that, for any ε>0, the measure Q can be chosen so that dQdP≤1+ε.