2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/126844We give a very short and rather elementary proof of Gromov's filling volume inequality for n-dimensional Lipschitz cycles (with integer and Z_2-coefficients) in $L^\infty$-spaces. This inequality is used in the proof of Gromov's systolic inequality for closed aspherical Riemannian manifolds and is often regarded as the difficult step therein.4 pagesDifferential Geometry53C23text