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A nonzero left-invariant regular Borel measure on a locally compact Hausdorff group, unique up to positive scale; right Haar measure is analogous, and a left Haar measure is also right-invariant precisely for unimodular groups.
Left Haar measure is unique up to positive scale. Right Haar measure is analogous; a left Haar measure is also right-invariant precisely when the group is unimodular.
wp-haar_measurenlab-haar_measuremathlib-haar-measureEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Every locally compact Hausdorff topological group admits a nonzero left Haar measure, unique up to multiplication by a positive scalar.
Feed several structures into a construction junction and impose compatibility between them.
wp-haar_measurenlab-haar_measuremathlib-haar-measureEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Invariant integration over compact groups underlies group averaging, lattice gauge theory, and representation orthogonality.
A mathematical concept supplies part of the formal language, state space, representation, or analytic machinery used by a scientific or mathematical-physics concept. The source is the mathematical predecessor; this does not claim that physical content follows from mathematics alone.
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