Zapiski Nauchn. Semin. POMI,

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

**Abstract.**
Let $\tau$ be a probability measure on $[0,1]$. We consider
a generalization of the classic Dirichlet process -
the random probability measure
$F=\sum P_i\delta_{X_i}$, where $X=\{X_i\}$ is a sequence of
independent random variables with the common distribution
$\tau$ and $P=\{P_i\}$ is independent of $X$ and
has the two-parameter Poisson-Dirichlet
distribution $PD(\alpha,\theta)$ on the unit simplex.
The main result is the formula connecting the distribution
$\mu$ of the random mean value $\int xdF(x)$
with the parameter measure $\tau$.

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