Talk:Falconer's conjecture
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Regarding the "Related Conjectures" section.
I believe Erdős' conjecture has been disproven in Edgar, Gerald A. and Chris Miller. “Borel subrings of the reals.” (2002), which specifically states that given a subring of the reals, E, that is also a Borel set, either E is the entirety of the reals or E has Hausdorff dimension 0. Doubinsky (talk) 15:26, 10 June 2024 (UTC)