Probability Space of Stochastic Fractals

  • Yu. P. Virchenko
  • O. L. Shpilinskaya


We develop a general method for the construction of a probability structure on the space F of random sets in ℝ. For this purpose, by using the introduced notion of c-system, we prove a theorem on the unique extension of a finite measure from a c-system to the minimal c-algebra. The obtained structure of measurability enables one to determine probability distributions of the c-algebra of random events sufficient, e.g., for the so-called fractal dimensionality of random realizations to be considered as a measurable functional on F.
How to Cite
Virchenko, Y. P., and O. L. Shpilinskaya. “Probability Space of Stochastic Fractals”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, no. 11, Nov. 2004, pp. 1467-84,
Research articles