When we define a general poisson point process, we ask for the measure to be a Radon measure and I don't understand why do we ask this.
Why can't we define a general poisson point process only using a regular measure $\mu$ and defining the probability of the number of arrivals $N$ in a set $B$ to be $\mathbb P(N(B)=k)=e^{-\mu(B)}\frac{\mu(B)^k}{k!}$ ? What is and why do we ask of a Radon measure ?