a measure of students' autonomy can make them better prepare

学生一定的自理能力能够让他们更好地进入成年人的生活,因为学生可以有自主决策和批判思维的能力.
a measure of在这里是degree of sth; some （事物的）程度, 地步的意思,看例句: She achieved a measure of success with her first book. 她的第一部书就获得了一定程度的成功.
better prepared for 是让.更好地为...准备,我的译文是意译