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On a problem of Erdős on similar copies of sequences in measurable sets

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If you have a question about this talk, please contact Yonatan Gutman.

More than 40 years ago Erdős asked whether there exists an infinite set S of real numbers such that every measurable set of positive measure contains a subset similar to S. This question is still open. It is also open in the case when S is the sequence 1/2^n.

I will review what is known about this problem, including the finite combinatorial problem to which it can be transformed, and why sequences converging to zero slower than geometric fail.

I will also talk about my contribution that there exists a sequence S such that every measurable set of positive measure contains subsets similar to almost every random perturbation of S.

This talk is part of the Discrete Analysis Seminar series.

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