In the topology and group theory, subdivisions of mathematics, a local compact group is a topological group G, which is locally compact as a topological space. Local compact groups are important because they have a natural size called the Haar size. This Hair size allows you to define Integrons for functions on G.
Many of the results of the representation theory for finite groups are proven by taking the average over the group. These evidence can be transferred to locally compact groups by replacing the average with the Haar integral. The resulting theory forms a central part of the harmonic analysis. The theory of local compact abelse groups is described by Pontryagin duality, a generalized fourier transformation.
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