2003/08/04 by Sergio Albeverio, Albeverio Sergio, Sergio, Albeverio +3 · 1 citation
Mathematics · #30B20 #60G30 #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Equations Stability Results #Mathematical Dynamics and Fractals #Mathematical and Theoretical Analysis #Probability (math.PR) #math.DS #math.PR #msc:30B20 #msc:60G30
paper · pdf · doi:10.48550/arxiv.math/0308025
15 pages
openalex publication_date 2003/08/04 · arxiv created 2003/08/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We examine measure preserving mappings f acting from a probability space (Ω, F,μ) into a probability space % (Ω*,F*,μ*) , where μ*=μ(f-1). Conditions on f, under which f preserves the relations ''to be singular'' and ''to be absolutely continuous'' between measures defined on (Ω, F) and corresponding image measures, are investigated. We apply the results to investigate the distribution of the random variable % ξ=∑∞k=1 ξkλk, where % λ∈ (0;1), and ξk are independent not necessarily identically distributed random variables taking the values i with probabilities % pik ,i=0,1. We also studied in details the metric-topological and fractal properties of the distribution of a random variable ψ= ∑∞k=1 ξkak, where ak>0 are terms of the convergent series.