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Tangents of σ-finite curves and scaled oscillation

Published online by Cambridge University Press:  28 January 2016

MARIANNA CSÖRNYEI  and
BOBBY WILSON
MARIANNA CSÖRNYEI
Affiliation:
Department of Mathematics, University of Chicago, 5734 S. University Avenue, Chicago, IL 60637, U.S.A. e-mail: [email protected]; [email protected]
BOBBY WILSON
Affiliation:
Department of Mathematics, University of Chicago, 5734 S. University Avenue, Chicago, IL 60637, U.S.A. e-mail: [email protected]; [email protected]
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Abstract

We show that every continuous simple curve with σ-finite length has a tangent at positively many points. We also apply this result to functions with finite lower scaled oscillation; and study the validity of the results in higher dimension.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 161 , Issue 1 , July 2016 , pp. 1 - 12
Copyright
Copyright © Cambridge Philosophical Society 2016 

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References

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