locally compact group meaning: definition, quotations

locally compact group

noun

Mathematics, Sciences, Topology A topological group whose underlying topology is both locally compact and Hausdorff.

Indeed, if there is one property of locally compact groups more responsible than any other for the rich positive content of their representation theory, it is their possession of left-invariant and right-invariant (Haar) measures. The connection between the representation theory of a locally compact group and that of general Banach algebras proceeds directly from Lebesgue integration with respect to Haar measure on the group.1988, J. M. G. Fell, R. S. Doran, Representations of *-Algebras, Locally Compact Groups, and Banach *-Algebraic Bundles, Volume 1, Academic Press, page 63:
A locally compact group G is called Lie projective if it is the projective limit #92;textstyle#92;underset#123;#92;leftarrow#125;#123;#92;lim#125;#95;#123;#92;alpha#92;in#92;mathbb#123;A2012, H. Heyer, Probability Measures on Locally Compact Groups, Springer, page 12:

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Let G be a locally compact group and H a closed subgroup of G, and suppose that #92;pi and #92;tau are irreducible representations of G and H, respectively.2013, Eberhard Kaniuth, Keith F. Taylor, Induced Representations of Locally Compact Groups, Cambridge University Press, page 269: