Absolute and conditional convergence of series in Franklin systems (Q920336)

The following theorem is proved. The series \(\sum^{\infty}_{n=0}a_ nf_ n(x)\), where \(\{f_ n(x)\}^{\infty}_{n=0}\) is the Franklin system, is unconditionally convergent a.e. on a set \(E\subset [0,1]\), \(| E| >0\), iff \(\sum^{\infty}_{n=0}| a_ nf_ n(x)| <\infty\) for almost every \(x\in E\).