∫ f dμ defined via simple functions approximating f from below; agrees with Riemann where both are defined, but handles a strictly larger class (e.g., Dirichlet function). Core of modern analysis.
Lebesgue integral
Related concepts
- Lebesgue measure
- Riemann integral
- Dominated convergence theorem
- Fubini theorem
- Lp space
- Radon-Nikodym theorem
- Riemann integral
- Random variable
- Expectation E[X]
- Absolute continuity
- Monotone convergence theorem
- Fatou's lemma
- Measure-preserving transformation
- Lebesgue differentiation theorem
- Distribution theory (Schwartz)