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A Constructive Examination of Rectifiability
Stockholm University, Faculty of Science, Department of Mathematics.
Stockholm University, Faculty of Science, Department of Mathematics.
2016 (English)In: Journal of Logic and Analysis, ISSN 1759-9008, E-ISSN 1759-9008, Vol. 8, UNSP 4Article in journal (Refereed) Published
Abstract [en]

We present a Brouwerian example showing that the classical statement 'Every Lipschitz mapping f : [0; 1] -> [0; 1] has rectifiable graph' is essentially nonconstructive. We turn this Brouwerian example into an explicit recursive example of a Lipschitz function on [0; 1] that is not rectifiable. Then we deal with the connections, if any, between the properties of rectifiability and having a variation. We show that the former property implies the latter, but the statement 'Every continuous, real-valued function on [0; 1] that has a variation is rectifiable' is essentially nonconstructive.

Place, publisher, year, edition, pages
2016. Vol. 8, UNSP 4
Keyword [en]
Constructive/recursive analysis, Lipschitz, rectifiable, Brouwerian example, recursive counterexample
National Category
Mathematics
Research subject
Mathematical Logic
Identifiers
URN: urn:nbn:se:su:diva-140112DOI: 10.4115/jla.2016.8.4ISI: 000395233500002OAI: oai:DiVA.org:su-140112DiVA: diva2:1077516
Available from: 2017-02-27 Created: 2017-02-27 Last updated: 2017-11-29Bibliographically approved

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