Boolean algebras and uniform convergence of series ✩

Several classical results on uniform convergence of unconditionally Cauchy series are generalized to weakly unconditionally Cauchy series. This uniform convergence is characterized through subalgebras and subfamilies of P(N). A generalization of the Orlicz–Pettis theorem is also proved by mean of subalgebras of P(N).  2003 Elsevier Inc. All rights reserved