Every locally compact topological group has a nonzero translation-invariant regular measure, unique up to scale. On a compact group it can be normalized to have total mass one.
The Haar measure is an important concept in the area of harmonic analysis and abstract algebra, specifically in the context of topological groups. It is a way of defining a measure on a locally compact topological group that is left-invariant (or right-invariant), which means it remains unchanged (invariant) under the group's operations.
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