Let [begin{aligned}g_{a}^{(u)} & =sup left{t: B_{t}+u t=a ight} T_{a}^{(u)} & =inf left{t: B_{t}+u t=a ight}end{aligned}] Prove that

Let

\[\begin{aligned}g_{a}^{(u)} & =\sup \left\{t: B_{t}+u t=a\right\} \\T_{a}^{(u)} & =\inf \left\{t: B_{t}+u t=a\right\}\end{aligned}\]

Prove that

\[\left(T_{a}^{(u)}, g_{a}^{(u)}\right) \stackrel{\text { law }}{=}\left(\frac{1}{g_{u}^{(a)}}, \frac{1}{T_{u}^{(a)}}\right)\]