Let $\mu$ a probability measure on $\mathbb{R}$, we define the Stieltjes transform by : $$ S[\mu](\lambda)=\int_\mathbb{R} \frac{d\mu(t)}{t-\lambda} $$ For all $\lambda\in\Omega:=\mathbb{C}-\mathbb{R}$.
For which conditions $S$ will be injective, from the set of probability measure to the set of holomorphic functions on $\Omega$ ?