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Preprint Number 2286
2286. Amador Martin-Pizarro, Daniel Palacin and Julia Wolf Stability, corners, and other 2-dimensional shapes E-mail: Submission date: 25 October 2022 Abstract: We introduce a relaxation of stability, called robust stability, which is insensitive to perturbations by subsets of Loeb measure $0$ in a pseudofinite group. We show that robust stability satisfies a stationarity principle for measure independent elements. We apply this principle to deduce the existence of squares and $L$-shapes in dense subsets of Cartesian squares of pseudofinite groups, possibly non-abelian. Our results imply qualitative asymptotic versions for Cartesian squares of finite groups. Mathematics Subject Classification: 03C13, 03C45, 11B30 Keywords and phrases: |
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