I am studying an article in which convolution is used very much and it is used between all sorts of objects: functions, distributions and measures. I know that convolving a $L^1$ function (for example) with a regularizing kernel we get a smooth function. That's how we prove the density of the space of functions with compact support in $L^1$.
But how should I think of the convolution of a distribution with a regularizing kernel? Or the convolution of a measure with a regularizing kernel?
I haven't found any good and short introduction on the subject. If you have in mind some documents/books which provide a good introduction to the theory of convolution of distributions and measures, they are welcome. Thank you.