Let $X$ be a smooth manifold, and let $u,v \in \mathcal{D}'(X)$ be distributions. Suppose that there do not exist a point $x \in X$ and a nonzero covector $\xi \in T_x^*X$ such that
Let $\Delta: X \to X \times X$ be the diagonal embedding, defined by $\Delta(x)=(x,x)$. Then the product distribution $uv \in \mathcal{D}'(X)$ is well-defined by