A construction on Lie groups On an n-dimensional Lie group, Haar measure can be constructed easily as the measure induced by a left-invariant n-form. Source: Internet
Halmos rather confusingly uses the term "Borel set" for elements of the σ-ring generated by compact sets, and defines Haar measure on these sets. Source: Internet
However something like it does work for almost periodic functions on the group which do have a mean value, though this is not given by with respect to Haar measure. Source: Internet
Construction of Haar measure A construction using compact subsets The following method of constructing Haar measure is more or less the method used by Haar and Weil. Source: Internet
However, with a right instead of a left Haar measure, the latter integral is preferred over the former. Source: Internet
Indeed, for a Borel set S, let us denote by the set of inverses of elements of S. If we define : then this is a right Haar measure. Source: Internet