= Convolution of p-adic measures
{title2=$(\mu*\nu)(h)=\int\!\int h(xy)\,d\mu(x)\,d\nu(y)$}
On a <profinite group>, convolution is first defined for functions on a finite quotient by summing products of the two measures' coset coefficients, then extended by uniform approximation. Finite-quotient associativity proves associativity. For an abelian <group> it is commutative; the Dirac measure at the identity is the identity element. Under the <measure realization of an Iwasawa algebra>, it becomes group-algebra multiplication.
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