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Let   E   be a finite‐dimensional normed space and   Ω   a non‐empty convex open set in   E  . We show that the Lipschitz‐free space of   Ω   is canonically isometric to the quotient ofL  1    (  Ω  ,  E  )by the subspace consisting of vector fields with zero divergence in the sense of distributions on   E  .

ISOMETRIC REPRESENTATION OF LIPSCHITZ‐FREE SPACES OVER CONVEX DOMAINS IN FINITE‐DIMENSIONAL SPACES