2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/223452To each function $f$ of bounded quadratic variation ($f\in V_2$) we associate a Hausdorff measure $μ_f$. We show that the map $f\toμ_f$ is locally Lipschitz and onto the positive cone of $\mathcal{M}[0,1]$. We use the measures $\{μ_f:f\in V_2\}$ to determine the structure of the subspaces of $V_2^0$ which either contain $c_0$ or the square stopping time space $S^2$.36 pages This is a revised version with few typos and linguistic correctionsFunctional Analysis28A78, 46B20, 46B26text