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Using a description of the topology of the spaces ${\mathbf{E}}^{\text{'}}\left(\Omega \right)$ ($\Omega$ open convex subset of $R^n$) via the Fourier transform, namely their analytically uniform structures, we arrive at a formula describing the convex hull of the singular support of a distribution $T$, $T\in {\mathbf{E}}^{\text{'}}$. We give applications to a class of distributions $T$ satisfying $$\text{cv.}\text{sing.}\text{supp.}S*T=\text{cv.}\text{sing.}\text{supp.}S+\text{cv.}\text{sing.}\text{supp.}T$$ for all $S\in {\mathbf{E}}^{\text{'}}$.