An author in a paper suggests that a binary function f(x) can be expressed as
$f(x) = 1_\Omega(x)$
where $f(x) \in \{0,1\}$ for all $ x \in R^2$
$\Omega$ is an arbitrary bounded measurable subset of $R^2$
What does he mean when he expresses $f(x)$ as $1_\Omega(x)$ ?