The Sharp Hausdorff Measure Condition for Length of Projections
نویسندگان
چکیده
In a recent paper, Pertti Mattila asked which gauge functions φ have the property that for any Borel set A ⊂ R2 with Hausdorff measure Hφ(A) > 0, the projection of A to almost every line has positive length. We show that finiteness of ∫ 1 0 φ(r) r2 dr, which is known to be sufficient for this property, is also necessary for regularly varying φ. Our proof is based on a random construction adapted to the gauge function.
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