## 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 $S^2$.## References

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## Bibliographic Information

**D. Apatsidis**- Affiliation: Department of Mathematics, Faculty of Applied Sciences, National Technical University of Athens, Zografou Campus, 157 80, Athens, Greece
- Email: dapatsidis@hotmail.com
**S. A. Argyros**- Affiliation: Department of Mathematics, Faculty of Applied Sciences, National Technical University of Athens, Zografou Campus, 157 80, Athens, Greece
- MR Author ID: 26995
- Email: sargyros@math.ntua.gr
**V. Kanellopoulos**- Affiliation: Department of Mathematics, Faculty of Applied Sciences, National Technical University of Athens, Zografou Campus, 157 80, Athens, Greece
- Email: bkanel@math.ntua.gr
- Received by editor(s): March 31, 2009
- Received by editor(s) in revised form: July 14, 2009
- Published electronically: March 15, 2011
- Additional Notes: This research was supported by PEBE 2007.
- © Copyright 2011 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**363**(2011), 4225-4262 - MSC (2000): Primary 28A78, 46B20, 46B26
- DOI: https://doi.org/10.1090/S0002-9947-2011-05209-8
- MathSciNet review: 2792986