Forward-measure terminal rate in a linear bond model (${\mathbb{E}}^{Q^T}[r_T\mid {\mathcal{F}}_t]=e^{-(T-t)}{r}_t/P(t,T)$)

For the bounded rate diffusion of linear bond pricing in a bounded short-rate diffusion, $D_t{e}^{-(T-t)}{r}_t$ is a bounded martingale with terminal value $D_T{r}_T$. Dividing its conditional expectation by $D_{t}P(t,T)$ through the Bayes formula for conditional expectation gives the displayed forward-measure expectation. It lies between zero and one.