Abstract
We shall present here two examples from “geometric Ramsey theory” which illustrate how ergodic theoretic techniques can be used to prove that subsets of Euclidean space of positive density necessarily contain certain configurations. Specifically we will deal with subsets of the plane, and our results will be valid for subsets of “positive upper density”.
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Fürstenberg, H., Katznelson, Y., Weiss, B. (1990). Ergodic Theory and Configurations in Sets of Positive Density. In: Nešetřil, J., Rödl, V. (eds) Mathematics of Ramsey Theory. Algorithms and Combinatorics, vol 5. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-72905-8_13
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DOI: https://doi.org/10.1007/978-3-642-72905-8_13
Publisher Name: Springer, Berlin, Heidelberg
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