Probability Space of Stochastic Fractals
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.
English version (Springer): Ukrainian Mathematical Journal 56 (2004), no. 11, pp 1748-1765.
Citation Example: Shpilinskaya O. L., Virchenko Yu. P. Probability Space of Stochastic Fractals // Ukr. Mat. Zh. - 2004. - 56, № 11. - pp. 1467-1484.