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LeanPool.EhrhartVolumeInequality.Convergence

Ehrhart volume inequality: Convergence #

The final concentration argument and Ehrhart volume inequality.

theorem Ehrhart.Volume.ehrhart_volume_inequality_for_sets {n : ℕ} (hn : 0 < n) (S : Set (Space n)) (hconvex : Convex ℝ S) (hcompact : IsCompact S) (hinterior : (interior S).Nonempty) (hcentered : barycenter S = 0) (hlattice : interiorLatticePoints S = {0}) :
normalizedVolume S ≤ (↑n + 1) ^ n / ↑n.factorial

Ehrhart's sharp volume inequality for a centered convex body with one interior lattice point.