Let $\mu$ be a finite measure on $\mathbb{R}$. What is the definition of the operator $d$ in the expression: $d\mu$. For example, I have an exercise where at one point:
\begin{equation} d\mu(x) = \frac{d x}{1+x^2} \end{equation}
I would said this a "differential" of $\mu$, but I can not find any definition of this kind on the Internet.
This is a notation related to Radon-Nykodym theorem. In this context, this means that for each non-negative measurable function, $$\int_{\mathbb R}f(x)d\mu(x)=\int_{\mathbb R}\frac{f(x)}{1+x^2}dx.$$