A local integrable function \(v\in L^1_{\text{loc}}(\Omega)\) defines a distribution . To be more precise, it can be associated with the following map
\begin{equation*} v(\varphi)=\int_{\Omega} v \varphi, \end{equation*}where \(\varphi\in \mathcal{D}(\Omega)\) is a test function .