µ(B) for all open set B with p(aB) = 0. In fact every Borel subset can be decomposed as 0 0 0 B =B U(B n 8B) with p(B) = µ(B), and a BC aB. Theorem 3 does not extend immediately to vector valued measures. For example consider the sequence of signed measures An := 81/n - 6_1/n E M(IR) .
Cartesian Currents in the Calculus of Variations I: Cartesian Currents (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge A Series of Modern Surveys in Mathematics) by Mariano Giaquinta