The unique translation-invariant complete measure on ℝⁿ assigning interval [a,b] measure b−a. Constructed via the Carathéodory extension from outer measure. Measures all Borel sets plus Lebesgue-null completions.
Lebesgue measure
Related concepts
- σ-algebra F
- Real numbers (ℝ)
- Lebesgue integral
- Probability measure P
- Borel set
- Measurable function
- Signed measure
- Product measure
- Haar measure
- Birkhoff ergodic theorem
- Bochner integral
- Descriptive set theory
- Geometric measure theory
- Carathéodory extension theorem
- Radon-Nikodym theorem
- Fubini-Tonelli theorem
- Monotone convergence theorem
- Dominated convergence theorem
- Fatou's lemma
- Lᵖ duality