This is an announcement for the paper "Hausdorff measures and functions of bounded quadratic variation" by D.Apatsidis, S.A.Argyros, and V.Kanellopoulos. Abstract: To each function $f$ in the space $V_2$ we associate a Hausdorff measure $\mu_f$. We show that the map $f\to\mu_f$ is locally Lipschitz and onto the positive cone of $\mathcal{M}[0,1]$. We use the measures $\{\mu_f:f\in V_2\}$ to determine the structure of the subspaces of $V_2^0$ which either contain $c_0$ or the square stopping time space $S^2$. Archive classification: math.FA Mathematics Subject Classification: 28A78, 46B20, 46B26 Remarks: 36 pages The source file(s), haus_quad2.tex: 141123 bytes, is(are) stored in gzipped form as 0903.2809.gz with size 38kb. The corresponding postcript file has gzipped size 219kb. Submitted from: sargyros@math.ntua.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0903.2809 or http://arXiv.org/abs/0903.2809 or by email in unzipped form by transmitting an empty message with subject line uget 0903.2809 or in gzipped form by using subject line get 0903.2809 to: math@arXiv.org.