In both my book, and on Wikipedia they define convulution of two measures like this:
$(\mu_1*\mu_2)(B)=\int_{\mathbb{R}^d}\mathcal{X}_B(x+y)d\mu_1(x)d\mu_2(y)$
It doesn't seem like a typo, but why do they use $\int_{\mathbb{R}^d}$ instead of $\int_{(\mathbb{R}^d)^2}$ or $\int_{\mathbb{R}^d}\int_{\mathbb{R}^d}$? The same sources seem to use this last notation(which is common) when they talk about "doubleintegration" of a function, integration over a product measure etc.. But aren't we here also working with a double integral? Can you please explain why the notation is how it is?