How can I show that the $p$-variation of a standard Brownian motion is infinite almost surely for any $p > 1/2$. By this I mean the total variation,
$lim_{\delta\to0} (sup_{\pi:\delta(\pi)=\delta} \sum_{j=1}^{N(\pi)}$$|B(t_j)-B(t_{j-1})|^p)$,
where $\delta(\pi)$ is the mesh of the partition $\pi$.