Define the correlation integral as C(ϵ) congruent lim_(N->∞) 1/N^2 sum_(i, j = 1 i!=j)^∞ H(ϵ - left bracketing bar x_i - x_j right bracketing bar ), where H is the Heaviside step function. When the below limit exists, the correlation dimension is then defined as D_2 congruent d_cor congruent lim_(ϵ, ϵ'->0^+) (ln[(C(ϵ))/(C(ϵ'))])/(ln(ϵ/ϵ')). If ν is the correlation exponent, then lim_(ϵ->0) ν->D_2.

capacity dimension | correlation exponent | information dimension | q-dimension