Distributions can be viewed as derivatives of continuous functions, see Rudin's book on Functional Analysis. This representation has several drawbacks:

• One cannot read off the order of a distribution,

• nor the support,

• the representation is not unique.

More generally, one can say that every distribution (also on manifolds and vector bundles thereon) can be written as a sum of derivatives of Radon measures.

My question is: can this representation be made unique, by, say, insisting that each summand be of minimal order? In that case, can one read off the support as being equal to the support of the involved measures? Likewise for the order as being the maximal order of derivation?