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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Hausdorff measures and functions of bounded quadratic variation
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by D. Apatsidis, S. A. Argyros and V. Kanellopoulos PDF
Trans. Amer. Math. Soc. 363 (2011), 4225-4262 Request permission

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 $S^2$.
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Additional 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