= Bochner consistency identity for convolution squares
{c}
{title2=$\widehat p\,\mu_q=\widehat q\,\mu_p=\mu_{p*q}$}
For finite sums of compactly supported convolution squares, $\widehat p,\widehat q\geq0$. Insert the <Bochner theorem> representation of $q$ into $p*q$ and apply the <Fubini theorem>: its representing measure is $\widehat p\,\mu_q$. Reversing $p,q$ and using uniqueness gives the displayed identity. It makes the local quotients $\mu_p/\widehat p$ consistent wherever $\widehat p>0$.
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