ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Alphabet
Deduction system
Theory
Zermelo-Fraenkel set theory
Set
Binary cartesian set product
Binary relation
Map
Function
Measure
Real measure
Euclidean real measure
Complex measure
Basic measure
Unsigned basic measure
Outer measure
Lebesgue outer measure
Lebesgue set
Lebesgue sigma-algebra
Lebesgue measurable space
Definition D1743
Lebesgue measure
Formulation 0
Let $M = (\mathbb{R}^n, \mathcal{L})$ be a D1742: Lebesgue measurable space.
Let $\mu^*$ be the D780: Lebesgue outer measure on $\mathbb{R}^n$.
The Lebesgue measure on $M$ is the D992: Function \begin{equation} \mathcal{L} \to [0, \infty], \quad E \mapsto \mu^*(E) \end{equation}
Results
R1064: Isotonicity of Lebesgue measure