Abstract :

In mathematical analysis, the Haar measure assigns an "invariant volume" to subsets of locally compact topological groups, consequently defining an "integral" for functions on those groups. This measure was introduced by Alfred Haar in 1933, though its special case for Lie groups had been introduced by Adolf Hurwitz in 1897 under the name "invariant integral". Haar measures are used in many parts of analyis, number theory, group theory, representation theory,statistics, probability theory and ergodic theory. In this talk, we shall discuss the existence and uniqueness of the Haar measure on a locally comapct topological group.