ABSTRACT

We call u the differential norm on D. Although v is not a proper norm because it may attain the value oo it nevertheless defines d ifferential convergence in Ο by

verify that the summable differentials form a Riesz subspace S of D with v a finite Riesz norm on S. We contend that S is a Banach lattice under v. We need only prove completeness

means that for ση = Σ ί=ιΡΐ, ση —* σ as defined by (2).