 Not only the recipe for the computation of the volume element formula_67 depends on the chosen parameters, but also the final result, i.e.the analytic form of the weight function (measure) formula_68.For instance, the Euler angle parametrization of SO(3) gives the weight formula_69 while the n, ψ parametrization gives the weight formula_70
with formula_71

It can be shown that the irreducible matrix representations of compact Lie groups are finite-dimensional and can be chosen to be unitary