No arbitrage is possible, over any given time horizon, relative to a strategy \nu that has the numeraire property (either with respect to the underlying probability measure \mathbb{P}, or with respect to any other probability measure which is equivalent to \mathbb{P}).
A probability measure \mathbb{Q} is called equivalent martingale measure (EMM) on a given time-horizon [0,T], if it has the same null sets as \mathbb{P} on \mathcal{F}_T, and if the processes X_1(t), \dots, X_n(t) with 0 \leq t \leq T are all \mathbb{Q}−martingales.