Measure and integration Measures Concept
Almost everywhere
Summary
A property of the points of a measure space holds almost everywhere if the points where it fails lie in a set of measure zero. Most statements about integrals and measurable functions only hold, and only need to hold, almost everywhere. In probability theory the same notion is called almost surely.
Where this leads
15 pages build on this one.
- Scheffé's lemma
- Egorov's theorem
- Lp space
- L-infinity space
- Weak Lp space
- Lorentz space
- Dominated convergence theorem
- Vitali convergence theorem
- Radon–Nikodym derivative
- Riesz's subsequence theorem
- Fundamental theorem of calculus for Lebesgue integrals
- Lebesgue differentiation theorem
- Poincaré recurrence theorem
- Lebesgue's density theorem
- Orlicz space
Further reading
About this page
| Tag | RARTMA0ZEC |
|---|---|
| URI | m2://RARTMA0ZEC |
| Kind | concept |
| Writing | W0 stub |
| MSC | 28A12, 28A20 |
| Same as | |
| Changed | 2 November 2026 |
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What this page needs for W1
- a source with a locator (0 of 1)
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What links here
Used by
- Scheffé's lemma
- Egorov's theorem
- Lp space
- L-infinity space
- Weak Lp space
- Lorentz space
- Dominated convergence theorem
- Vitali convergence theorem
- Radon–Nikodym derivative
- Riesz's subsequence theorem
- Fundamental theorem of calculus for Lebesgue integrals
- Lebesgue differentiation theorem
- Poincaré recurrence theorem
- Lebesgue's density theorem
- Orlicz space