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A forward measure is the martingale measure associated with taking a zero-coupon bond as numéraire. Prices divided by that bond are martingales under the corresponding measure.

A martingale deflator is a strictly positive adapted process whose product with each cum-dividend asset gain is a local martingale. After normalization by a numéraire, a martingale deflator determines an equivalent martingale measure.

A T-forward measure is a probability measure $Q^T$, equivalent to the physical measure, under which prices expressed in units of the positive maturity-$T$ bond are martingales. Equivalently, every attainable payoff $X_T$ has time-$t$ priceThe zero-coupon bond is the numéraire.

For a maturity $T$, the T-forward measure uses the zero-coupon bond maturing at $T$ as numéraire. If $B_t^T$ is its time-$t$ price, an attainable payoff $X_T$ has value $B_t^T{\mathbb{E}}_{Q^T}[X_T\mid {\mathcal{F}}_t]$.