Bounded Multiplier Convergence in Measure of Random Vector Series
C. Ryll-Nardzewski, Wojbor A. Woyczyński · Proceedings of the American Mathematical Society · 1975
If the series $\Sigma {f_i}$ of random vectors with values in a Banach space converges unconditionally in measure, then, for each $({\lambda _i})\epsilon {l^\infty }$, the series $\Sigma {\lambda _i}{f_i}$ also converges unconditionally in measure.