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We give a genuinely n-dimensional construction of uniformly elliptic operators L in M" (of divergence form, and of nondivergence form), which have positive .L-harmonic measures on a class of porous sets on dW\_ with zero surface measure. The porosity condition given is sharp. The earlier methods were all two dimensional.doi:10.1090/s0002-9947-1994-1260206-0 fatcat:orw5eaxgpneexpizkkuapy4q24