4
$\begingroup$

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 $1_\Omega(x)$ ?

1 Answers 1

6

This is called Indicator function; it means that $f(x) = 1$ if $x \in \Omega$, and $f(x) = 0$ if $x \notin \Omega$.

  • 1
    (3) In category theory, you may see $1_\Omega$ meaning the identity function on $\Omega$.2011-06-03