Definition 30.4.1 (Convolution of Measures).label Let $G$ be a locally compact group, and $\mu, \nu \in M_{R}(G; \complex)$ be finite Radon measures, then the convolution of $\mu$ and $\nu$ is the Radon measure $\mu * \nu$ defined by
\[\int_{G}\phi(x)(\mu * \nu)(dx) = \iint_{G \times G}\phi(xy)\mu(dx)\nu(dy)\]
for all $\phi \in C_{c}(G; \complex)$[1].
- There seem to be some subtleties with having to take the Radon product here.keyboard_return
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