User:IntegralPython/sandbox/Fractal measure
Fractal measure is a generalization of the concepts of length, area, and volume to non-integer dimensions, especially in application towards fractals. There is no unique fractal measure, in part although not entirely due to the lack of a unique definition of fractal dimension; the most common fractal measures include the hausdorff measure and the packing measure, based off of the hausdorff dimension and packing dimension respectively.[1] Fractal measures are measures in the sense of measure theory, and are usually defined to agree with the n-dimensional Lebesgue measure when n is an integer.[2]
Hausdorff measure
Packing measure
References