Let $F : \mathbb{R} \to \mathbb{R}$ be a D4364: Real function such that

(i)	$F$ is a D3249: Right-continuous function
(ii)	$F$ is a D5321: Standard-isotone basic real function
(iii)	$\mu^*_F$ is a D1858: Stieltjes outer measure with respect to $F$
(iv)	$\mathcal{S}$ is a D1860: Stieltjes sigma-algebra on $\mathbb{R}$ with respect to $F$

The Stieltjes measure with respect to $F$ is the D4361: Unsigned basic function \begin{equation} \mathcal{S} \to [0, \infty], \quad E \mapsto \mu^*_F(E) \end{equation}