A one dimensional poisson point process (PPP) $N$ has intensity measure $\Lambda(0,x)$ and we want to find the following $$E\left[\prod_{x\in N} e^{-\frac{s}{x}}\right]$$ using the definition of probability generating functional we can write as $$E\left[\prod_{x\in N} e^{-\frac{s}{x}}\right]=\exp\left(\int_0^{\infty}\left(e^{-\frac{s}{x}}-1\right)\Lambda(0,dx)\right)$$ I want to know what is actually $\Lambda(0,dx)$. Is it the derivative of $\Lambda(0,x)$?
Edit:
Please provide the expression that results after applying the integration by parts on the following expression $$\exp\left(\int_0^{\infty}\left(e^{-\frac{s}{x}}-1\right)\Lambda(0,dx)\right)$$ and please assume that $u=\left(e^{-\frac{s}{x}}-1\right)$ in the famous formula of integration by parts $\int udv=uv-\int vdu$. Thanks in advance