Sunday, 23 November 2008

fa.functional analysis - Do all graphs of C1 functions have Hausdorff dimension 1?

Let fcolonItomathbbR. Since f is C1, the graph Gammaf is locally bilipschitz to I, via the projection. It follows that Hausdorff dimension is the same as that of I (being defined in terms of the metric space structure only), so it is 1.



Disclaimer: I haven't seen these topics for quite a while, so I may have said something stupid.

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