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?

The affine map $h$ is invertible, with inverse $h^{-1}(x) = h(x)$. So $$h^{-1}(x_0 - A) = h(x_0 - A) = 2x_0 - (x_0 - A) = x_0 + A.$$

Added Later: The question has been edited so that $A \subset \mathbb{R}$ rather than $A \in \mathbb{R}$. 
Now $x_0 - A$ denotes the set $\{x_0 - a \mid a \in A\}$ and $x_0 + A$ denotes the set $\{x_0 + a \mid a \in A\}$. Given a function $f : X \to Y$, and a subset $S \subset X$, then $f(S)$ denotes the subset $\{f(s) \mid s \in S\}$ of $Y$. So,
$$h^{-1}(x_0 - A) = \{h^{-1}(x_0 - a) \mid a \in A\} = \{h(x_0 - a) \mid a \in A\} = \{x_0 + a \mid a \in A\} = x_0 + A.$$
