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
50 pages build on this one.
- Abelian theorems for integral transforms
- Fourier transform on Schwartz space
- Ergodic decomposition
- Discrete series representation
- Oscillator representation
- Hardy's uncertainty principle
- Scheffé's lemma
- Smoothing by convolution
- Strichartz estimates in Lorentz space
- Egorov's theorem
- Lp space
- L-infinity space
- Weak Lp space
- Kingman's subadditive ergodic theorem
- Cantor–Lebesgue theorem
- Derivative of a convolution
- Lorentz space
- Dominated convergence theorem
- Vitali convergence theorem
- Entropic uncertainty principle
- Integral operator
- Furstenberg's multiple recurrence theorem
- Radon–Nikodym derivative
- Heisenberg inequality for the Fourier transform
- Carleson's theorem
- Babenko–Beckner inequality
- Differentiation and multiplication under the Fourier transform
- Shannon–McMillan–Breiman theorem
- Birkhoff's ergodic theorem
- Kac's lemma
- Riesz's subsequence theorem
- Fundamental lemma of the calculus of variations
- Laplace transform tends to zero at infinity
- Hunt's extension of Carleson's theorem
- Oseledets theorem
- Cantor's uniqueness theorem for trigonometric series
- Muckenhoupt weights
- Conservative system
- Fundamental theorem of calculus for Lebesgue integrals
- Lebesgue differentiation theorem
- Fourier inversion theorem
- Poincaré recurrence theorem
- Pesin theory
- Lebesgue's density theorem
- Mellin's inverse formula
- Fisher–Neyman factorization theorem
- Symmetric and self-reciprocal kernels
- Stone–von Neumann theorem
- Orlicz space
- Fourier transform of the Gaussian
Further reading
About this page
| Tag | RARTMA0ZEC |
|---|---|
| URI | m2://RARTMA0ZEC |
| Kind | concept |
| Writing | W0 stub |
| MSC | 28A12, 28A20 |
| Same as |
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What links here
Used by
- Scheffé's lemma
- Egorov's theorem
- Lp space
- L-infinity space
- Weak Lp space
- Kingman's subadditive ergodic theorem
- Lorentz space
- Dominated convergence theorem
- Vitali convergence theorem
- Radon–Nikodym derivative
- Carleson's theorem
- Shannon–McMillan–Breiman theorem
- Birkhoff's ergodic theorem
- Riesz's subsequence theorem
- Fundamental lemma of the calculus of variations
- Hunt's extension of Carleson's theorem
- Oseledets theorem
- Muckenhoupt weights
- Fundamental theorem of calculus for Lebesgue integrals
- Lebesgue differentiation theorem
- Fourier inversion theorem
- Poincaré recurrence theorem
- Lebesgue's density theorem
- Orlicz space