Measure and integration The Lebesgue integral Concept
Integrable function
Summary
A measurable function on a measure space is integrable when the integral of its absolute value is finite. These are the functions for which the Lebesgue integral is a well-defined finite number. Integrable functions form the space , and the convergence theorems of integration are stated for them.
Where this leads
14 pages build on this one.
- Scheffé's lemma
- Pettis integral
- Hardy–Littlewood maximal function
- Lebesgue point
- Dominated convergence theorem
- Vitali convergence theorem
- Lebesgue–Stieltjes integration
- Uniform integrability
- Jensen's inequality for integrals
- Fundamental theorem of calculus for Lebesgue integrals
- Lebesgue differentiation theorem
- Riemann–Lebesgue lemma
- Lebesgue integral
- Absolute continuity of the Lebesgue integral
Further reading
About this page
| Tag | X7GTF3D98F |
|---|---|
| URI | m2://X7GTF3D98F |
| Kind | concept |
| Writing | W0 stub |
| MSC | 28A25, 26A42 |
| Changed | 2 November 2026 |
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Used by
- Scheffé's lemma
- Pettis integral
- Hardy–Littlewood maximal function
- Lebesgue point
- Dominated convergence theorem
- Vitali convergence theorem
- Lebesgue–Stieltjes integration
- Uniform integrability
- Jensen's inequality for integrals
- Fundamental theorem of calculus for Lebesgue integrals
- Lebesgue differentiation theorem
- Riemann–Lebesgue lemma
- Lebesgue integral
- Absolute continuity of the Lebesgue integral