Hausdorff measures and functions of bounded quadratic variation

Apatsidis, D.; Argyros, S.; Kanellopoulos, V.

doi:10.1090/S0002-9947-2011-05209-8

Hausdorff measures and functions of bounded quadratic variation
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by D. Apatsidis, S. A. Argyros and V. Kanellopoulos

Trans. Amer. Math. Soc. 363 (2011), 4225-4262

DOI: https://doi.org/10.1090/S0002-9947-2011-05209-8

Published electronically: March 15, 2011

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Abstract:

To each function $f$ of bounded quadratic variation 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 $S^2$.

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