How constructive is constructing measures?
Arno Pauly, Willem L. Fouch\'e
TL;DR
This paper investigates the computational complexity of constructing measures supported on sets, especially Frostman measures, and classifies these tasks within the Weihrauch lattice, also determining the Weihrauch degree of Hausdorff dimension.
Contribution
It provides a classification of measure construction problems in the Weihrauch lattice and analyzes the computational complexity of Frostman measures and Hausdorff dimension.
Findings
Classifies measure construction tasks in the Weihrauch lattice
Determines the Weihrauch degree of Hausdorff dimension
Analyzes the complexity of constructing Frostman measures
Abstract
Given some set, how hard is it to construct a measure supported by it? We classify some variations of this task in the Weihrauch lattice. Particular attention is paid to Frostman measures on sets with positive Hausdorff dimension. As a side result, the Weihrauch degree of Hausdorff dimension itself is determined.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Topology and Set Theory · Computability, Logic, AI Algorithms