A paper by de Philippis and Rindler, titled On the Structure of $\mathscr{A}$-Free Measures and Applications, opens as follows:
Let $\mu$ be a Radon measure on $\mathbb{R}^d$ with values in $\mathbb{R}^m$ that is $\mathscr{A}$-free for a $k$th order linear constant-coefficient PDE operator $\mathscr{A}$, i.e. $$ \mathscr{A}\mu = \sum_{|\alpha| \leq k}A_\alpha \partial^\alpha \mu. $$ Here $A_\alpha$ is an $n \times m$ (real-valued) matrix and $\alpha = (\alpha_1, \ldots, \alpha_d)$ is a multi-index.
Sadly, I cannot move past this first sentence. I know basic measure theory and PDE theory, and if anyone is able to help answer my question, it would be much appreciated.
Basically, I don't even know what on earth the partial derivative of a measure is. I hear my professor mention that it is made sense of through the theory of distributions. I have looked at some resources on distributions, but have not yet seen any mention of PDE operators in them (perhaps I have not looked long enough, though). So my question is, what does the operator $\mathscr{A}$ even mean? An additional question after this would be, what does it mean for a measure $\mu$ to be $\mathscr{A}$-free, although clearly this comes after the former question.
If anyone could help answer, or perhaps refer me to a resource, that would be wonderful.