Measure and integration Measures Concept
Measure
Summary
A measure on a measurable space is a function that gives each measurable set a size in . It gives the empty set size and is countably additive: the size of a countable disjoint union is the sum of the sizes. Measures generalize length, area, volume, counting and probability, and they are the basis of the Lebesgue integral.
Where this leads
42 pages build on this one.
- Absolutely continuous measure
- Newtonian space
- Restriction of a measure
- S-finite measure
- Finite measure
- Measure space
- Contiguity of measures
- Fuzzy measure
- Product measure
- Kantorovich duality
- Integral geometry
- Borel measure
- Indeterminate moment problem
- Positivity of Hankel matrices of moments
- Loeb measure
- Moment problem
- Brenier's theorem
- Sigma-finite measure
- Integral operator
- Green's function of a Markov process
- Quasi-invariant measure
- Hahn–Kolmogorov theorem
- Hausdorff moment problem
- Continuity of measure from below and above
- Determinate moment problem
- Invariant measure
- Optimal transport and the Monge problem
- Measure algebra
- Vitali–Hahn–Saks theorem
- Displacement convexity
- Krein's condition
- Carathéodory's extension theorem
- Mutually singular measures
- Carleman's condition
- Hamburger moment problem
- Measure with density
- Jordan decomposition of a signed measure
- Lebesgue–Stieltjes measure
- Non-atomic measure
- Stieltjes moment problem
- Nevanlinna parametrization of solutions
- Pushforward measure
Further reading
About this page
| Tag | PR11BZQQPG |
|---|---|
| URI | m2://PR11BZQQPG |
| Kind | concept |
| Writing | W0 stub |
| MSC | 28A12, 28A10 |
| Same as |
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What links here
Special cases
- Complete measure
- Finite measure
- Loeb measure
- Borel measure
- S-finite measure
- Non-atomic measure
- Sigma-finite measure
- Measure with density
Used by
- Absolutely continuous measure
- Newtonian space
- Restriction of a measure
- S-finite measure
- Finite measure
- Measure space
- Fuzzy measure
- Product measure
- Integral geometry
- Borel measure
- Indeterminate moment problem
- Positivity of Hankel matrices of moments
- Loeb measure
- Moment problem
- Sigma-finite measure
- Green's function of a Markov process
- Quasi-invariant measure
- Hahn–Kolmogorov theorem
- Hausdorff moment problem
- Continuity of measure from below and above
- Determinate moment problem
- Invariant measure
- Measure algebra
- Vitali–Hahn–Saks theorem
- Carathéodory's extension theorem
- Mutually singular measures
- Hamburger moment problem
- Measure with density
- Jordan decomposition of a signed measure
- Lebesgue–Stieltjes measure
- Non-atomic measure
- Stieltjes moment problem
- Pushforward measure