2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/100814We show that C^1 hypersurfaces in the Heisenberg group are countably N-rectifiable. As a corollary, this shows that all C^1_H graphs over the xy-plane are countable N-rectifiable, showing the equivalence of this notion of rectifiability with that of Franchi, Serra Cassano and Serapioni for such surfaces.8 pages, new version adds expository material and context to introduction and simplifies one aspect of the proof of the main theoremDifferential GeometryMetric Geometry53C17text