I have a question regarding the correct notation when integrating the Dirac distribution $\mu$. When treating it as a measure, I can write the Lebesgue inetgral $\int_{\mathbb{R}}\mu(dx)=1.$ What if I wish to treat $\mu$ as a distribution? Would I write $\int_{-\infty}^{\infty}d\mu(x)=1?$ If correct, what sort of integral would this be?
Thanks...