# Commit 2021-10-04 09:48 ab7d2519

View on Github →feat(measure_theory/covering/besicovitch_vector_space): vector spaces satisfy the assumption of Besicovitch covering theorem (#9461)
The Besicovitch covering theorem works in any metric space subject to a technical condition: there should be no satellite configuration of `N+1`

points, for some `N`

. We prove that this condition is satisfied in finite-dimensional real vector spaces. Moreover, we get the optimal bound for `N`

: it coincides with the maximal number of `1`

-separated points that fit in a ball of radius `2`

, by [Füredi and Loeb, On the best constant for the Besicovitch covering theorem][furedi-loeb1994]