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 $
