On the existence of a nonzero mass density for a fractal set of independent pointlike masses with a power-type distribution
The concept of global mass density (GMD) for deterministic and stochastic fractals is considered. For the construction of stochastic fractal, the Lévy-Mandelbrot algorithm and its modification are used. The probability density of GMD is investigated for all these cases. The main result is that this distribution has a nondegenerate limit under the following condition on the connection between the exponent of mass distribution and fractal dimension \(D=3\alpha\).
scientific article; zbMATH DE number 1289194