Probability Space of Stochastic Fractals

• Date: 2004
• Main Authors: Virchenko, Yu. P., Shpilinskaya, O. L., Вирченко, Ю. П., Шпилинская, О. Л.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2004
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3859
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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 structur...