Exponential void probabilities forbid fixed atoms
= Exponential void probabilities forbid fixed atoms
If bounded intervals have void <probabilities> $e^{-\lambda(I)}$ for <Lebesgue measure> $\lambda$, a fixed deterministic point $x$ has zero chance of being an atom. Surround it by intervals of lengths tending to zero and use $\mathbb P(M(\{x\})>0)\leq1-e^{-\lambda(I)}$. This holds for each fixed endpoint, not simultaneously for all real points of a nonempty point process.