(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 $F$ |

**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}