Zapiski Nauchn. Semin. POMI,

English translation: J. Math. Sci. (N.Y.),

**Abstract.**
Given a sequence $x$ of points in the unit interval, we associate
with it a virtual permutation $w=w(x)$ (that is, a sequence $w$
of permutations $w_n \in \frak S_n$ such that $w_{n-1}=w_n'$ is
obtained from $w_n$ by erasing the last element $n$ from its
cycle, for all $n=1,2,\,\ldots$). We introduce a detailed version
of the well-known stick breaking process, generating a random
sequence $x$. It is proved that the associated random virtual
permutation $w(x)$ has Ewens' distribution. Up to subsets of
zero measure, the space $\frak S^\infty = \varprojlim \frak S_n$
of virtual permutations is identified with the cube
$[0,1]^\infty$.

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