On Weyl Multipliers of Almost Everywhere Unconditional Convergence of Series With Respect to General Haar and Franklin Systems

We obtain necessary and sufficient conditions for an increasing nonnegative sequence $\omega_n$, $n\in\mathbb{N}$, to be a Weyl multiplier for a.e. unconditional convergence for general Haar or Franklin systems corresponding to an admissible sequence ${\cal T}$.