ThmDex – An index of mathematical definitions, results, and conjectures.
F11076
Formulation 1
Let $\mathbb{R}^D$ be a D816: Euclidean real Cartesian product such that
(i) $\ell^*$ is a D780: Lebesgue outer measure on $\mathbb{R}^D$
Then \begin{equation} \forall \, E, F \subseteq \mathbb{R}^D \left( E \subseteq F \quad \implies \quad \ell^*(E) \leq \ell^*(F) \right) \end{equation}