 This says that distributions are not particularly exotic objects; they are only as complicated as necessary.If "f" ∈ "S"′(R"n") is a tempered distribution, then there exists a constant "C" > 0, and positive integers "M" and "N" such that for all Schwartz functions "formula_1" ∈ "S"(R"n")

This estimate along with some techniques from functional analysis can be used to show that there is a continuous slowly increasing function "F" and a multi-index "α" such that

If "f" ∈ D′(R"n"), then for any compact set "K" ⊂ R"n", there exists a continuous function "F " compactly supported 
in R"n" (possibly on a larger set than "K" itself) and a multi-index "α" such that "f" = "D""α""F" on Cc∞("K").This follows from the previously quoted result on tempered distributions by means of a localization argument.