with Lebesgue measure $|B|>0$ and a measurable space $({\mathbf N},{\mathcal N})$ of integer-valued finite measures on $B.$ ${\mathcal N}$ is the smallest $\sigma $-algebra which makes the mappings ${\mathbf x}\mapsto {\mathbf x}(A)$ measurable for all Borel sets $A\subset B$ and all ${\mathbf x}\in {\mathbf N}.$ A random element having a.s. values in $({\mathbf N},{\mathcal N})$ is called a finite point process. Integer-valued finite measures can be represented by systems of points corresponding to their support. Let a Poisson point process $\eta $ on $B$ have finite intensity measure $\lambda $ with no atoms, $\lambda (B)>0,$ and distribution $P_\eta $ on $\mathcal N.$ For a measurable map $F:{\mathbf N}\rightarrow {\mathbb R}$ it holds [@RefA] $$\label{odhad} {\mathbb E}[F(\eta )]=e^{-\lambda (B)}\sum_{n=0}^\infty\frac{1}{n!}\int_B\dots\int_B F(u_1,\dots ,u_n)\lambda^n ({\text{\rm d}}(u_1,\dots ,u_n)),$$ where we write $\lambda^n ({\text{\rm d}}(x_1,\dots ,x_n))$ instead of $\lambda ({\text{\rm d}}x_1)\dots\lambda ({\text{\rm d}}x_n).$ Further we consider a finite point process $\mu $ on $B$ given by a density $p$ w.r.t. $\eta ,$ i.e. with distribution $P_\mu $ $$\label{dns}dP_\mu ({\mathbf x})=p({\mathbf x})dP_\eta ({\mathbf x}),\; {\mathbf x}\in \mathbf N,$$ where $p:{\mathbf N}\rightarrow {\mathbb R}_+$ is measurable satisfying $$\int_{\mathbf N}p({\mathbf x}){\text{\rm d}}P_\eta ({\mathbf x})=1.$$ The consequence of (\[dns\]) is a formula $$\label{odha}{\mathbb E}F(\mu )={\mathbb E}[F(\eta )p(\eta )].$$ Let $\mu 