Hausdorff Measures and Functions of Bounded Quadratic Variation

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

Hausdorff Measures and Functions of Bounded Quadratic Variation

Authors

Apatsidis, D.

Argyros, S. A.

Kanellopoulos, V.

Description

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 $S^2$.
36 pages This is a revised version with few typos and linguistic corrections