If $A \subset \mathbb{R}$, $x_0 \in \mathbb{R}$ and $h$ is an affine map, what does $h^{-1}(x_0 - A)$ mean? I am reading a book, and it suddenly says:

A distribution $\nu$ is symmetric around a point $x_0 \in \mathbb{R}$ if $h(\nu) = \nu$ where $h$ is the affine map given by $h(x) = 2x_0 - x$. As $h^{-1}(x_0 - A) = x_0 + A$ for $A \subset \mathbb{R}$ ...

What does that mean?

It's just the inverse of $h(x)$.  Call it $y$:
$$y = 2x_0 - x \to x = 2x_0 - y = h^{-1}(y)$$
$$h^{-1}(x_0 - A) = 2x_0 - (x_0 - A) = x_0 + A.$$
