A divergence measure vectorfield is an ℝ n valued measure on an open subset U of ℝ n whose weak divergence in U is a (signed) measure. The paper uses the product rule for the product of the divergence measure by a function from W 1,∞ (U) 3 established in Šilhavý [Šilhavý, M., submitted, 2007] to prove the divergence theorem for the divergence measure vectorfields on bounded open sets U. It is shown that the surface integral of the normal component of the vectorfield occurring in the classical divergence theorem has to be replaced by a continuous linear functional on the space of Lipschitz functions on the boundary1 the volume integral contains the duality pairing occurring in the product rule. The boundary of U is arbitrary, it can be even fractal in the sense that the normal to ∂U cannot be defined.