What does $_{x \in A}$ mean?

Question

What does $_{x \in A}$ mean?

I have found it in this document. I thought initially that the result was a vector, but in the formula it appears to be a real number.

Answer 1

Indicator function. Defined by $$ _{x \in A}(y) = \begin{cases} 1 & y \in A \\ 0 & y \notin A \end{cases} $$

Alternative notation: $_A$ or $\chi_A$.