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As a consequence, if $X=(X_1,...,X_N)$ is a $M^N$-valued random variable with absolutely continuous law, then almost surely $\\mu(X(\\om))$ has a unique $p$-mean. In particular if $(X_n)_{n\\ge 1}$ is an independent sample of an absolutely continuous law in $M$, then the process $e_{p,n}(\\om)=e_p(X_1(\\om),..., X_n(\\om))$ is well-defined. 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