Pluripolarity of sets with small Hausdorff measure

We show that any set E subset of C-n, n greater than or equal to 2, with finite Hausdorff measure Lambda ((log 1/r)-n) (E) < + infinity is pluripolar. The result is sharp with respect to the measuring function. The new idea in the proof is to combine a construction from potential theory, related to the real variational integral integral(Omega)\del u \(m), Omega subset of R-m, with properties of the piuricomplex relative extremal function for the Bedford-Taylor capacity.