This is an announcement for the paper "Burkholder-Gundy-Davis inequality in martingale Hardy spaces with variable exponent" by Peide Liu and Maofa Wang. Abstract: In this paper, the classical Dellacherie's theorem about stochastic process is extended to variable exponent Lebesgue spaces. As its applications, we obtain variable exponent analogues of several famous inequalities in classical martingale theory, including convexity lemma, Burkholder-Gundy-Davis' inequality and Chevalier's inequality. Moreover, we investigate some other equivalent relations between variable exponent martingale Hardy spaces. Archive classification: math.FA Submitted from: pdliu@whu.edu.cn The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1412.8146 or http://arXiv.org/abs/1412.8146