In particular, the Fourier transform of the constant function equal to 1 is the "δ" distribution. The formal definition of distributions exhibits them as a subspace of a very large space, namely the topological dual of D("U") (or S(R"d") for tempered distributions). It is not immediately clear from the definition how exotic a distribution might be. To answer this question, it is instructive to see distributions built up from a smaller space, namely the space of continuous functions. Roughly, any distribution is locally a (multiple) derivative of a continuous function. A precise version of this result, given below, holds for distributions of compact support, tempered distributions, and general distributions. Generally speaking, no proper subset of the space of distributions contains all continuous functions and is closed under differentiation. 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. If "f" has support at a single point {"P"}, then "f" is in fact a finite linear combination of distributional derivatives of the "δ" function at "P". That is, there exists an integer "m" and complex constants "a""α" for multi-indices |"α"| ≤ "m" such that  where τ"P" is the translation operator. A version of the above theorem holds locally in the following sense . Let "T" be a distribution on "U", then one can find for every multi-index "α" a continuous function "g""α" such that  and that any compact subset "K" of "U" intersects the supports of only finitely many "g""α"; therefore, to evaluate the value of "T" for a given smooth function "f" compactly supported in "U", we only need finitely many "g""α"; hence the infinite sum above is well-defined as a distribution.