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Who Asked Us? How the Theory of Computing Answers Questions about Analysis

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Complexity and Approximation

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12000))

Abstract

Algorithmic fractal dimensions—constructs of computability theory—have recently been used to answer open questions in classical geometric measure theory, questions of mathematical analysis whose statements do not involve computability theory or logic. We survey these developments and the prospects for future such results.

J.H. Lutz—Research supported in part by National Science Foundation grants 1545028 and 1900716.

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Authors and Affiliations

  1. Iowa State University, Ames, IA, USA

    Jack H. Lutz & Neil Lutz

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  1. Jack H. Lutz
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Correspondence to Jack H. Lutz .

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Editors and Affiliations

  1. The University of Texas at Dallas, Richardson, TX, USA

    Ding-Zhu Du

  2. University of Massachusetts Lowell, Lowell, MA, USA

    Jie Wang

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Dedicated to the Memory of Ker-I Ko

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Lutz, J.H., Lutz, N. (2020). Who Asked Us? How the Theory of Computing Answers Questions about Analysis. In: Du, DZ., Wang, J. (eds) Complexity and Approximation. Lecture Notes in Computer Science(), vol 12000. Springer, Cham. https://doi.org/10.1007/978-3-030-41672-0_4

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  • DOI: https://doi.org/10.1007/978-3-030-41672-0_4

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