This definition generalizes the one for sets as one can see by taking formula_31 for any formula_5 as in that section. It also accounts for the reflected paraboloid example above because for formula_33 we have formula_34 with multiplicity two. The notion of approximate tangent spaces is very closely related to that of rectifiable sets. Loosely speaking, rectifiable sets are precisely those for which approximate tangent spaces exist almost everywhere. The following lemma encapsulates this relationship:  Lemma. Let formula_1 be measurable with respect to "m"-dimensional Hausdorff measure. Then formula_5 is m-rectifiable if and only if there exists a positive locally formula_2-integrable function formula_38 such that the Radon measure  has approximate tangent spaces formula_40 for formula_2-almost every formula_42.