ABSTRACT
Given an integrable differential σ > 0 on a cell K the set of all absolutely integrable differentials of the form f a is the L ebesgue space C\ = £ i(K , a). It is easy to see that C\ is a Riesz subspace of the Banach lattice of all absolutely integrable differentials on K . (See Theorem 3 (§2.4) and the ensuing dis cussion there.) To conclude that C\ is a Banach lattice under the norm i'{ fa ) = f K \ f \a we must prove that C\ is complete. The series formulation of completeness is again convenient.
