For Barański carpets, the Hausdorff measure at the critical dimension is either finite and positive or infinite, with a new uniform-fibre condition (u.f.H) deciding which case occurs.
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The Hausdorff measure and uniform fibre conditions for Bara\'nski carpet
For Barański carpets, the Hausdorff measure at the critical dimension is either finite and positive or infinite, with a new uniform-fibre condition (u.f.H) deciding which case occurs.