2. Theory of Dimension II: “Metric” Dimensions

2.1 Hausdorff-Besicovitch Dimension

The Hausdorff-Besicovitch dimension is useful for studying structurally complex sets, particularly fractals (see below). Unlike the dimensions discussed above, the Hausdorff dimension can also take on non-integer real values.

Definition (Hausdorff-Besicovitch dimension). The Hausdorff-Besicovitch dimension of a nonempty subset X of ${ℝ}_2^n$ is a positive real number, zero, or possibly infinity, denoted by dim _HB ...