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The Teichmüller space of the Hirsch foliation
This function is called the Ahlfors function of K. Its existence can be proved by using a normal family argument involving Montel's theorem. Let dim H denote Hausdorff dimension and H 1 denote 1-dimensional Hausdorff measure.
However, this conjecture is false. A counterexample was first given by A.
Vitushkin , and a much simpler one by J.
Related Vitushkin’s Conjecture for Removable Sets (Universitext)
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