I will introduce a general method in dealing with Fourier decay of random measures arising from Kahane's T-martingale theory, thus including Mandelbrot Cascades (canonical or microcanonical), Gaussian Multiplicative Chaos, Random Coverings and more abstract ones. This very new method is a combination of many fundamental vector-valued martingale inequalities such as martingale type inequality, Burkholder-Rosenthal inequality, Bourgain-Stein inequality etc and also an idea which seems to related to the decoupling method in harmonic analysis. The talk is based on joint works with Xinxin Chen, Yong Han, Zipeng Wang, and with Zhaofeng Lin, Mingjie Tan.