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For more reading on examples of Haar measures: https://en.wikipedia.org/wiki/Haar_measure#Examples | For more reading on examples of Haar measures: https://en.wikipedia.org/wiki/Haar_measure#Examples | ||
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Revision as of 00:00, 7 December 2020
Examples
If a Haar measure is done on the topological group $ {\displaystyle (\mathbb {R} ,+)} $ (meaning the set is all real numbers and the binary operation is addition), the Haar measure takes the value of 1 on the closed interval from zero to one and is equal to a Lebesgue measure taken on the Borel subsets to all real numbers. This can be generalized to any dimension.
If the group G is all nonzero real numbers, then the Haar measure is given by $ \mu (S)=\int _{S}{\frac {1}{|t|}}\,dt $
For more reading on examples of Haar measures: https://en.wikipedia.org/wiki/Haar_measure#Examples
