ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

12. Probability and Statistics

1991 MS Classification: 28, 60 Kolumbán, J., Babes-Bolyai University, Cluj-Napoca, Romania Invariant sets in Menger spaces Hutchinson (1981) proved the following: Let X be a complete metric space and f_{1}, …, f_{m} : X → X be contraction maps. Then there exists a unique compact set K ⊆ X such that K = ⋃_{i=1}^{m} f_{i}(K). If the maps f_{i} are similitudes, this invariant set K is said to be self-similar. Our aim in this work is to generalize the above result for probabilistic metric spaces introduced in 1942 by K. Menger. We also prove some new results on the probabilistic Hausdorff-Pompeiu metric.