It is shown that every distribution on a compact interval can be identified to a relatively small class of nonstandard C-infinity functions, viz. finite-order derivatives of Bernstein polynomials of a fixed infinite order.

In every such class, functions share an intrinsic order of infinity, which restricts the fluctuations in their values.

The class of the delta-distribution is so small that, up to infinitesimals, there is only one function in it.