Let $G$ be an open set on some measure space $(\Omega,\Sigma, \mu)$. Show that the indicator function of $G$ is an increasing limit of a sequence of continuous functions.
I understand that this is a "simple text book exercise". I am only seeking for hints.
My idea (at least in 2D) is that we should construct some smooth trapezoidal-like functions, where the gradients near the endpoints of $G$ gets steeper and steeper.
Am I on the right track? Also, how do I write this out mathematically?