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arXiv · 0903.2809

Hausdorff Measures and Functions of Bounded Quadratic Variation

D. Apatsidis·S. A. Argyros·V. Kanellopoulos
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Abstract

To 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 $S^2$.

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D. Apatsidis, S. A. Argyros, V. Kanellopoulos. 2009-03-17. Hausdorff Measures and Functions of Bounded Quadratic Variation. https://arxiv.org/abs/0903.2809

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