 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 $\mathbb{P}(M(\{x\})>0)\le 1-e^{-\lambda (I)}$. This holds for each fixed endpoint, not simultaneously for all real points of a nonempty point process.