Meaning of locally compact group | Babel Free

Definitions

A topological group whose underlying topology is both locally compact and Hausdorff.

Equivalents

Examples

“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.”

“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;A”

“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.”

CEFR level