Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Image measures of infinite product measures and generalized Bernoulli
  convolutions   We examine measure preserving mappings $f$ acting from a probability space
$(\Omega, F,\mu) $ into a probability space $% (\Omega ^{*},F^{*},\mu ^{*}) ,$
where $\mu ^{*}=\mu (f^{-1})$. Conditions on $f$, under which $f$ preserves the
relations ''to be singular'' and ''to be absolutely continuous'' between
measures defined on $(\Omega, F) $ and corresponding image measures, are
investigated.
  We apply the results to investigate the distribution of the random variable
$% \xi =\sum\limits^{\infty}_{k=1} \xi_k\lambda ^k,$ where $% \lambda \in
(0;1),$ and $\xi_k$ 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 $\psi = \sum\limits^{\infty}_{k=1} \xi
_ka_k,$ where $a_k>0$ are terms of the convergent series.

18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex