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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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[[Category:MA271Fall2020Walther]]
 
[[Category:MA271Fall2020Walther]]

Latest revision as of 01:04, 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

Back to Walther MA271 Fall2020 topic18

Alumni Liaison

Ph.D. 2007, working on developing cool imaging technologies for digital cameras, camera phones, and video surveillance cameras.

Buyue Zhang