Haar measure (Q2782)
From MaRDI portal
left-invariant (or right-invariant) measure on locally compact topological group
- left Haar measure
- right Haar measure
- Haar integral
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Haar measure |
left-invariant (or right-invariant) measure on locally compact topological group |
|
Statements
1933
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![{\displaystyle \begin{aligned}&\mu\colon\operatorname{Borel}(G)\to[0,\infty]\\&\forall g\in G,S\in\operatorname{Borel}(G)\colon\mu(gS)=\mu(S)\\&\mu(S)=\inf\{\mu(U)\colon S\subset U\in\operatorname{Open}(G)\}=\sup\{\mu(K)\colon S\supset K\in\operatorname{Comp}(X)\end{aligned}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2d9d06d0e23c39a9db911978594eaca1497a686b)
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Identifiers
130805567
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C130805567
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Haar integral
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Haar_measure
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mathematics/haar-measure
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Definition:Haar_Measure
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