 Dominated martingale measure

For discounted one-period asset gains $Y$, a dominated martingale measure is a probability measure $Q$ absolutely continuous with respect to the physical probability measure $P$, under which the gains have zero expectation. Its Radon-Nikodym derivative $Z$ satisfies $Z\ge 0$, ${\mathbb{E}}_{P}Z=1$ and ${\mathbb{E}}_P[ZY]=0$. An equivalent martingale measure additionally has $Z>0$ almost surely. Absolute continuity permits some positive-probability physical states to receive zero pricing probability; equivalence does not.