1 Definition of Haar measures
A right Haar measure on is defined similarly, except with left translation invariance replaced by right translation invariance ( for all sets ). A bi-invariant Haar measure is a Haar measure that is both left invariant and right invariant.
2 Existence of Haar measures
For any discrete topological group , the counting measure on is a bi-invariant Haar measure. More generally, every locally compact topological group has a left Haar measure , which is unique up to scalar multiples. In addition, also admits a right Haar measure, and for an abelian group the left and right Haar measures are always equal. The Haar measure plays an important role in the development of Fourier analysis and representation theory on locally compact groups such as Lie groups and profinite groups.
|Date of creation||2013-03-22 12:40:55|
|Last modified on||2013-03-22 12:40:55|
|Last modified by||djao (24)|
|Defines||left Haar measure|
|Defines||right Haar measure|
|Defines||bi-invariant Haar measure|