Abstract
In the work the almost everywhere (a.e.) convergence (absolute convergence) of series by the general Haar and Franklin systems corresponding to weakly regular division of the segment \([0,1]\) are compared. It is proved that if a series by the general Haar system diverges (absolutely diverges) on a set \(E\) , then the series by the general Franklin system with the same coefficients diverges (absolutely diverges) a.e. in \(E\) . As a consequence, it is obtained that if a sequence \(\omega_{n}\) is not a Weyl multiplier for unconditional a.e. convergence of series by the general Haar system, then it is not a Weyl multiplier for unconditional a.e. convergence of series by the general Franklin series.
