# What does the notation $1_\Omega(x)$ mean?

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 $1_\Omega(x)$ ?

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This is called Indicator function; it means that $f(x) = 1$ if $x \in \Omega$, and $f(x) = 0$ if $x \notin \Omega$.
(2) Sometimes other notation is used: $\chi_\Omega$ for example, or the Knuth/Arrow notation $[\Omega]$ – GEdgar Jun 3 '11 at 13:22
(3) In category theory, you may see $1_\Omega$ meaning the identity function on $\Omega$. – GEdgar Jun 3 '11 at 13:23