Hausdorff Measures and Functions of Bounded Quadratic Variation

Details Hausdorff Measures and Functions of Bounded Quadratic Variation Hausdorff Measures and Functions of Bounded Quadratic Variation

2009-03-16

arxiv.org/abs/0903.2809v2

Mathematics

Functional Analysis

36 pages This is a revised version with few typos and linguistic corrections

Scientific paper

To each function $f$ of bounded quadratic variation ($f\in V_2$) 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 $S^2$.

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