Kovner–Besicovitch measure

In plane geometry the Kovner–Besicovitch measure is a number defined for any bounded convex set describing how close to being centrally symmetric it is.

It is the fraction of the area of the set that can be covered by its largest centrally symmetric subset.

is the center of symmetry of the largest centrally-symmetric set within a given convex body

[4] Branko Grünbaum writes that the Kovner–Besicovitch theorem was first published in Russian, in a 1935 textbook on the calculus of variations by Mikhail Lavrentyev and Lazar Lyusternik, where it was credited to Soviet mathematician and geophysicist S. S. Kovner [ru].

Additional proofs were given by Abram Samoilovitch Besicovitch and by István Fáry, who also proved that every minimizer of the Kovner–Besicovitch measure is a triangle.