A set E is right-sided weakly porous if and only if d(.,E)^(-α) belongs to the one-sided Muckenhoupt class A1+ for some α>0 and is locally integrable.
Geometry of sets and measures in Euclidean spaces , volume 44 of Cambridge Studies in Advanced Mathematics
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One-sided Muckenhoupt weights and one-sided weakly porous sets in $\mathbb{R}$
A set E is right-sided weakly porous if and only if d(.,E)^(-α) belongs to the one-sided Muckenhoupt class A1+ for some α>0 and is locally integrable.