### A constructive examination of rectifiability

#### Abstract

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.

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.

#### Full Text:

4. [PDF]DOI: https://doi.org/10.4115/jla.2016.8.4

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Journal of Logic and Analysis ISSN: 1759-9008