I have troubles understanding the definition of a random measure. Wikipedia says:
If $f$ is some measurable function on $\mathbb{R}^d$, then the sum of $f(x)$ over all the points $x\in N$ can be written as: $$ \int_{\textbf{N}} f(x) {N}(dx) $$ Where $ \textbf{N}$ is the space of all possible counting measures, hence putting an emphasis on the interpretation of $N$ as a random counting measure.
what does it mean that we integrate over the space of all possible counting measures? What exactly is the space of all possible (counting) measures? Can someone give me an examples of this space?