Image measures of infinite product measures and generalized Bernoulli convolutions
| dc.creator | Sergio, Albeverio | |
| dc.creator | Grygoriy, Torbin | |
| dc.date | 2003-08-04 | |
| dc.date | 2003-08-05 | |
| dc.date.accessioned | 2026-07-07T05:00:04Z | |
| dc.date.available | 2026-07-07T05:00:04Z | |
| dc.description | 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 $% ξ=\sum\limits^{\infty}_{k=1} ξ_kλ^k,$ where $% λ\in (0;1),$ and $ξ_k$ are independent not necessarily identically distributed random variables taking the values $i$ with probabilities $% p_{ik}$ ,$i=0,1.$ We also studied in details the metric-topological and fractal properties of the distribution of a random variable $ψ= \sum\limits^{\infty}_{k=1} ξ_ka_k,$ where $a_k>0$ are terms of the convergent series. | |
| dc.description | 15 pages | |
| dc.identifier | https://arxiv.org/abs/math/0308025 | |
| dc.identifier | http://arxiv.org/abs/math/0308025 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68236 | |
| dc.subject | Probability | |
| dc.subject | Dynamical Systems | |
| dc.subject | 60G30; 30B20 | |
| dc.title | Image measures of infinite product measures and generalized Bernoulli convolutions | |
| dc.type | text |