Measure and integration Measures on groups Concept
Haar measure
Summary
A Haar measure on a locally compact group is a nonzero Radon measure that does not change under left translation by elements of the group. Every locally compact group has one, and it is unique up to a positive constant. It extends Lebesgue measure on and counting measure on discrete groups, and it is the basic tool for integration and harmonic analysis on groups.
Where this leads
28 pages build on this one.
- Harmonic analysis on groups
- Discrete series representation
- Induced representation of a locally compact group
- Cantor group
- Hecke algebra of a locally compact group
- Peter–Weyl theorem
- Fourier transform on locally compact abelian groups
- Arthur–Selberg trace formula
- Group von Neumann algebra
- Lattice in a locally compact group
- Plancherel theorem for groups
- Group algebra of a locally compact group
- Schur orthogonality for compact groups
- Steinhaus theorem
- Harish-Chandra character
- Gelfand pair
- Spherical function
- Convolution
- Harish-Chandra's regularity theorem
- Complete reducibility of representations of compact groups
- Modular function
- Weyl integration formula
- Haar measure on a Lie group
- Wang's finiteness theorem
- Plancherel theorem for abelian groups
- Lie algebra of a compact group is reductive
- Unimodular group
- Lattice in a Lie group
Further reading
About this page
| Tag | VY0HXD3GC4 |
|---|---|
| URI | m2://VY0HXD3GC4 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 28C10, 22D05, 43A05 |
| Same as | |
| Changed | 2 November 2026 |
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Used by
- Harmonic analysis on groups
- Discrete series representation
- Induced representation of a locally compact group
- Cantor group
- Hecke algebra of a locally compact group
- Peter–Weyl theorem
- Fourier transform on locally compact abelian groups
- Arthur–Selberg trace formula
- Group von Neumann algebra
- Lattice in a locally compact group
- Plancherel theorem for groups
- Group algebra of a locally compact group
- Schur orthogonality for compact groups
- Steinhaus theorem
- Harish-Chandra character
- Gelfand pair
- Spherical function
- Convolution
- Harish-Chandra's regularity theorem
- Complete reducibility of representations of compact groups
- Modular function
- Weyl integration formula
- Haar measure on a Lie group
- Wang's finiteness theorem
- Plancherel theorem for abelian groups
- Lie algebra of a compact group is reductive
- Unimodular group
- Lattice in a Lie group