  We prove a sharp isoperimetric inequality for measured Finsler manifolds
having non-negative Ricci curvature and Euclidean volume growth. We also prove
a rigidity result for this inequality, under the additional hypotheses of
boundedness of the isoperimetric set and the finite reversibility of the space.
  As a consequence, we deduce the rigidity of the weighted anisotropic
isoperimetric inequality for cones in the Euclidean space, in the irreversible
setting.
