Abstract
We establish the inequality \(1/C_K(E)\ge \int_0^\infty |dK(t)|/N_E(t)\), where E is a compact metric space, K is a kernel function, CK is the associated capacity, and NE(t) denotes the minimal number of sets of diameter t needed to cover E. We give applications to the capacity of generalized Cantor sets, and to the capacity of δ-neighborhoods of a set. We also investigate possible converses to the inequality.
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