Arithmetic progressions in sets of fractional dimension
نویسندگان
چکیده
Let E ⊂ R be a closed set of Hausdorff dimension α. We prove that if α is sufficiently close to 1, and if E supports a probability measure obeying appropriate dimensionality and Fourier decay conditions, then E contains non-trivial 3-term arithmetic progressions. Mathematics Subject Classification: 28A78, 42A32, 42A38, 42A45, 11B25.
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تاریخ انتشار 2008