The Falconer distance conjecture
The following describes the scope of the Lean formalization related to the following accompanying paper(s):
Scope
The formalization proves the Falconer distance conjecture in every dimension. For every integer $d\ge2$ and compact set $E\subset\mathbb R^d$ with Hausdorff dimension greater than $d/2$, the set ${\lVert x-y\rVert:x,y\in E}$ has positive Lebesgue measure. The linked statements include both this all-dimensional result and the earlier planar case.
Comparator links
| Result | Comparator statement |
|---|---|
| Planar Falconer distance theorem | PlanarFalconer.lean |
| Falconer distance theorem in every dimension | FalconerAllDimensions.lean |