D_q congruent 1/(1 - q) lim_(ϵ->0) (ln I(q, ϵ))/(ln(1/ϵ), ) where I(q, ϵ) congruent sum_(i = 1)^N μ_i^q, ϵ is the box size, and μ_i is the natural measure. The capacity dimension (a.k.a. box-counting dimension) is given by q = 0, D_0 | = | 1/(1 - 0) lim_(ϵ->0) (ln( sum_(i = 1)^(N(ϵ)) 1))/(-ln ϵ) | = | -lim_(ϵ->0) (ln[N(ϵ)])/(ln ϵ). If all μ_is are equal, then the capacity dimension is obtained for any q.
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