Measure and integration Measures Concept
Pushforward measure
Summary
The pushforward measure moves a measure along a measurable function from one space to another. The new measure gives a set the old measure of its preimage. In probability theory, the distribution of a random variable is the pushforward of the probability measure along the variable. It also gives the abstract change of variables formula for integrals.
Where this leads
14 pages build on this one.
- Self-similar measure
- Kantorovich duality
- Brenier's theorem
- Quasi-invariant measure
- Duistermaat–Heckman formula
- Invariant measure
- Optimal transport and the Monge problem
- Disintegration theorem
- Gaussian measure
- Displacement convexity
- Cylinder set measure
- Cameron–Martin theorem
- Kolmogorov extension theorem
- Abstract Wiener space
Further reading
About this page
| Tag | 3N66TM3TSQ |
|---|---|
| URI | m2://3N66TM3TSQ |
| Kind | concept |
| Writing | W0 stub |
| MSC | 28A12, 28A20 |
| Same as |
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Used by
- Self-similar measure
- Brenier's theorem
- Quasi-invariant measure
- Duistermaat–Heckman formula
- Invariant measure
- Optimal transport and the Monge problem
- Disintegration theorem
- Gaussian measure
- Displacement convexity
- Cylinder set measure
- Cameron–Martin theorem
- Kolmogorov extension theorem
- Abstract Wiener space