Plancherel measure on set of irreducible representations of a finite group
Suppose is a finite group. Let be the set of irreducible representations (up to equivalence) of over the field of complex numbers. The Plancherel measure on this set assigns to each element of the measure where is the degree of the representation.
The Plancherel measure is a probability measure in the sense that the total measure of the set is . This follows from the fact that sum of squares of degrees of irreducible representations equals group order.