2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/131943We establish in this article convergence results of normalized Harder-Narasimhan polygons both in geometric and in arithmetic frameworks by introducing the Harder-Narasimhan filtration indexed by $\mathbb R$ and the associated Borel probability measure.Algebraic GeometryConvergence of Harder-Narasimhan polygonstext