Let $\mu$ be a finite measure on $(\mathbb R, \mathcal B(\mathbb R))$ and let $F_{\mu}: \mathbb R \rightarrow [0, \infty)$, $F_{\mu}(x) := \mu((- \infty, x])$.
If $F: \mathbb R \rightarrow [0, \infty)$ is bounded, monotone, right-continuous and $lim_{x \rightarrow - \infty} F(x) = 0$, then there exists exactly one measure $\mu$ on $(\mathbb R, \mathcal B(\mathbb R))$ such that $F = F_{\mu}$.
How can I show this statement?