  Small-angle scattering (SAS) data which show a succession of power-law decays
with decreasing values of scattering exponents, can be described in terms of
fractal structures with positive Lebesgue measure (fat fractals). In this work
we present a theoretical model for fat fractals and show how one can extract
structural information about the underlying fractal using SAS method, for the
well known fractals existing in the literature: Vicsek and Menger sponge. We
calculate analytically the fractal structure factor and study its properties in
momentum space. The models allow us to obtain the fractal dimension at each
structural level inside the fractal, the number of particles inside the fractal
and about the most common distances between the center of mass of the
particles.
