Hausdorff Measures and Functions of Bounded Quadratic Variation

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

Hausdorff Measures and Functions of Bounded Quadratic Variation

Functional Analysis 2009-03-17 v2

Authors: D. Apatsidis , S. A. Argyros , V. Kanellopoulos

Abstract

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 $S^2$ .

Keywords

Hausdorff measure bounded quadratic variation locally Lipschitz positive cone square stopping time space

Cite

@article{arxiv.0903.2809,
  title  = {Hausdorff Measures and Functions of Bounded Quadratic Variation},
  author = {D. Apatsidis and S. A. Argyros and V. Kanellopoulos},
  journal= {arXiv preprint arXiv:0903.2809},
  year   = {2009}
}

Comments

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

Hausdorff Measures and Functions of Bounded Quadratic Variation

Abstract

Keywords

Cite

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