In geometry, exterior dimension is a type of dimension that can be used to characterize the scaling behavior of "fat fractals".A fat fractal is defined to be a subset of Euclidean space such that, for every point of the set and every sufficiently small number ,the ball of radius centered at contains both a nonzero Lebesgue measure of points belonging to the fractal, and a nonzero Lebesgue measure of points that do not belong to the fractal. For such a set, the Hausdorff dimension is the same as that of the ambient space.