Marks, A., Dino, R., & Slaman, T. (2025). Hausdorff Dimension and Countable Borel Equivalence Relations. Proceedings of the American Mathematical Society.
We show that if E is a countable Borel equivalence relation on R n, then there is a closed subset A ⊆ [0, 1]n of Hausdorff dimension n so that E ↾ A is smooth. More generally, if ≤Q is a locally countable Borel quasi-order on 2ω and g is any gauge function of lower order than the identity, then there is a closed set A so that A is an antichain in ≤Q and Hg (A) > 0.
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Project title:
Algorithmische Komplexität von Strukturen und deren Äquivalenzrelationen: 101026834 (European Commission) Strukturen durch Lernen Klassifizieren: P 36781-N (FWF - Österr. Wissenschaftsfonds)
