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Computability and Set Theoretic Aspects of Hausdorff Dimension

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SASW09 - International conference on computability, complexity and randomness

The Hausdorff Dimension of a set of real numbers A is a numerical indication of the geometricfullness of A. Sets of positive measure have dimension 1, but there are null sets of every possibledimension between 0 and 1.   Effective Hausdorff Dimension is a variant which incorporates computability-theoreticconsiderations. By work of Jack and Neil Lutz, Elvira Mayordomo, and others, there is a directconnection between the the effective Hausdorff dimensions of the elements of a set A and theHausdorff dimension of A itself. We will describe how this point-to-set principle works, how allowsfor novel approaches to classical problems and further lines of investigation in Geometric MeasureTheory.

This talk is part of the Isaac Newton Institute Seminar Series series.

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