Let $F: \mathbb R \to \mathbb R$ be a continuous, bounded, non-decreasing and such that $\lim_{x \to - \infty} F(x) = 0$.
Can anybody show me why there exists a unique (!) measure $m_F$ on $(\mathbb R, B(\mathbb R))$ such that $m_F((- \infty, x]) = F(x)$ for any $x \in \mathbb R$?
(Where $B(\mathbb R)$ denotes the Borel $\sigma-$algebra on $\mathbb R$ induced by the Euclidean topology.)