Arithmetic progressions in sets of fractional dimension

Details Arithmetic progressions in sets of fractional dimension Arithmetic progressions in sets of fractional dimension

2007-12-22

arxiv.org/abs/0712.3882v2

Mathematics

Classical Analysis and ODEs

42 pages

Scientific paper

Let $E\subset\rr$ be a closed set of Hausdorff dimension $\alpha$. We prove
that if $\alpha$ is sufficiently close to 1, and if $E$ supports a
probabilistic measure obeying appropriate dimensionality and Fourier decay
conditions, then $E$ contains non-trivial 3-term arithmetic progressions.

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