Editing Haar measure (section)

{{Short description|Left-invariant (or right-invariant) measure on locally compact topological group}}
In [[mathematical analysis]], the '''Haar measure''' assigns an "invariant volume" to subsets of [[locally compact topological group]]s, consequently defining an [[integral]] for functions on those groups.

This [[Measure (mathematics)|measure]] was introduced by [[Alfréd Haar]] in 1933, though its special case for [[Lie groups]] had been introduced by [[Adolf Hurwitz]] in 1897 under the name "invariant integral".<ref name="Haar">{{Citation | first = A. | last = Haar | author-link = Alfréd Haar | title = Der Massbegriff in der Theorie der kontinuierlichen Gruppen | periodical = [[Annals of Mathematics]] | volume = 34 | series = 2 | issue = 1 | year = 1933 | pages = 147–169 |jstor=1968346 | doi=10.2307/1968346}}</ref><ref>I. M. James, History of Topology, p.186</ref> Haar measures are used in many parts of [[mathematical analysis|analysis]], [[number theory]], [[group theory]], [[representation theory]], [[mathematical statistics|statistics]], [[probability theory]], and [[ergodic theory]].