 The elements of formula_310can be identified as the space of distributions with compact support.Explicitly, if "T" is a distribution on "U" then the following are equivalent,
Compactly supported distributions define continuous linear functionals on the space C∞("U"); 
recall that the topology on C∞("U") is defined such that a sequence of test functions "formula_1""k" converges to 0 if and only if all derivatives of "formula_1""k" converge uniformly to 0 on every compact subset of "U".Conversely, it can be shown that every continuous linear functional on this space defines a distribution of compact support.