I am a newbie for Libor rates and all these questions...
Let be : $L(t,\delta)$ the Libor rate and $L_{t}(T,\delta)$ the forward Libor rate. Let's define : $Lb(T,\delta):=1+\delta L(T,\delta)=1/B(T,T+\delta)$ and $Lb_{t}(T,\delta):=1+\delta L_{t}(T,\delta)=B(t,T)/B(t,T+\delta)$. The question is to prove that under the forward measure of maturity $T+\delta$ that both $Lb_{t}(T,\delta)$ and $L_{t}(T,\delta)$ are local martingales. I began to define the forward measure of maturity $T+\delta$ (under which the numeraire is $B(T,T+\delta)$ ) :$Q^{T+\delta}$ but it's a lot of calculus. So how can we solve this ? Do we have to start from the model $dB(t,T)/B(t,T)=r_{t}dt+\Gamma (t,T)dW_{t}$ in order to define $dQ(t,T+\delta)=...dQ$ ?