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2 results on '"John Garnett"'

1. A doubling measure on $\mathbb {R}^d$ can charge a rectifiable curve.

Author

John Garnett, Rowan Killip, and Raanan Schul

Subjects
MEASURE theory, ALGEBRAIC curves, MATHEMATICAL analysis
Abstract

For $dgeq 2$, we construct a doubling measure $nu $ on $mathbb {R}^d$ and a rectifiable curve $Gamma $ such that $nu (Gamma )>0$. [ABSTRACT FROM AUTHOR]

Published
2009

2. Large sets of zero analytic capacity.

Author

John Garnett and Stan Yoshinobu

Subjects
CANTOR sets, HAUSDORFF measures
Abstract

We prove that certain Cantor sets with non-sigma-finite one-\linebreak dimensional Hausdorff measure have zero analytic capacity. [ABSTRACT FROM AUTHOR]

Published
2001
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