Every locally compact topological group has a nonzero translation-invariant regular measure, unique up to scale. On a compact group it can be normalized to have total mass one.
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- Averaging Kähler forms over a complex torus
- Complete reducibility of rational GL and SL representations
- Fourier transform over a local field
- Haar averaging produces invariant complements
- Haar twirling conditional expectation
- Orthogonalization of a compact-group representation
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- Radial kernel of the Kac collision operator
- Self-dual Haar measure
- Unitarization of a compact-group representation
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The Haar measure is an important concept in the area of harmonic analysis and abstract algebra, specifically in the context of topological groups. It is a way of defining a measure on a locally compact topological group that is left-invariant (or right-invariant), which means it remains unchanged (invariant) under the group's operations.