Abstract
AbstractWe show that the self-affine sets considered by McMullen in [11] and by Bedford in [1] have infinite Hausdorff measure in their dimension, except in the (rare) cases where the Hausdorff dimension coincides with the Minkowski (≡ box) dimension. More precisely, the Hausdorff measure of such a self-affine set K is infinite in the gauge(where γ is the Hausdorff dimension of K, and c > 0 is small). The Hausdorff measure of K becomes zero if 2 is replaced by any smaller number in the formula for the gauge ø.
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