Converting a differential form to a measure

Question

so today I was looking at the Generalized Stokes' Theorem: \begin{align} \intop_{\Omega} d\omega=\intop_{\partial\Omega}\omega\ \ , \end{align} where $\Omega$ is some region, and $\omega$ is a differential form. What I would like to know is how to convert a differential form into a measure. For example, I read in Choquet-Bruhat's Analysis, Manifolds, and Physics that there was a way to do this, but I am unsure on how to apply it in a more abstract setting. Any advice or help you can provide would be helpful, particularly in how it applies to the Generalized Stokes' Theorem.