A constructive examination of rectifiability

Douglas Bridges, Matthew Hendtlass, Erik Palmgren


We present a Brouwerian example showing that the classical statement 'every
Lipschitz mapping f from [0; 1] to [0; 1] has rectiable graph' is essentially non-
constructive. We turn this Brouwerian example into an explicit recursive ex-
ample of a Lipschitz function on [0; 1] that is not rectiable. Then
we deal with the connections, if any, between the properties of rectiability
and having a variation: we show that the former implies the latter, but the
statement every continuous, real-valued function on [0; 1] that has a variation
is rectiableis essentially nonconstructive.

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DOI: https://doi.org/10.4115/jla.2016.8.4

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Journal of Logic and Analysis ISSN:  1759-9008