= Compact continuous-derivative representation of a distribution
{title2=$u=\sum_\alpha\partial^\alpha f_\alpha$}
Every <compactly supported distribution> on an <open set> $X$ is a finite sum $u=\sum_\alpha\partial^\alpha f_\alpha$ with continuous $f_\alpha$ compactly supported inside $X$. One can first write $u=\partial^\gamma F$ for a continuous global <convolution> primitive, then multiply by a <cutoff function> equal to one near the support. The identity $\chi\partial^\gamma F=\sum_{\beta\leq\gamma}(-1)^{|\beta|}\binom\gamma\beta\partial^{\gamma-\beta}[(\partial^\beta\chi)F]$ localizes every coefficient. Finite global representation can fail for a <distribution of unbounded order>.
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