Let $n \in \mathbb{N}$ with $n \ge 1$, let $X \subset \mathbb{R}^n$ be open, let $\mathcal{L}^n$ denote $n$-dimensional [Lebesgue measure](/page/Lebesgue%20Measure) on $\mathbb{R}^n$, let $u \in \mathcal{D}'(X)$ be a distribution, identify each cotangent fibre $T_x^*X$ with $\mathbb{R}^n$ by the standard coordinate covectors $dx_1,\dots,dx_n$, and let $\pi: T^*X \setminus 0 \to X$ be the base projection defined by $\pi(x,\xi)=x$. Then

\begin{align*} \pi(WF(u)) = \operatorname{sing\,supp}(u). \end{align*}

Equivalently, for every $x_0 \in X$, the distribution $u$ is smooth in a neighbourhood of $x_0$ if and only if $(x_0,\xi_0) \notin WF(u)$ for every nonzero covector $\xi_0 \in \mathbb{R}^n \setminus \{0\}$.