The Besicovitch compression phenomenon and the Kakeya set conjecture
In 1919, Besicovitch constructed a compact set in the plane with Lebesgue measure 0 that contains a unit line segment pointing in every direction. Such objects are now called measure 0 Besicovitch sets (aka Kakeya sets). By replacing a measure zero Besicovitch set by its delta-thickening, one obtains a collectionContinue Reading

