Hausdorff dimension is a form of fractal dimension. Hausdorff measure ℋ^s is defined for each s>0 positive; when s is an integer, ℋ^s is a scalar multiple of Lebesgue measure ℒ^s. For any metric space X, there is a real number d such that ℋ^s (X) = ∞ for s<d and ℋ^s (X) = 0 for s>d. The number d is the Hausdorff dimension of X. For a compact metric space, it is always at least the topological dimension.