Before revision:  In this paper we overcome the difficulty by working with random locally convex modules endowed with the locally L^0 --convex topology rather than locally L^0--convex modules. Besides, some basic and key results in the FKV paper are also false so that some more interesting and essential things are covered, so we first correct these mistakes and further give a thorough treatment of random convex analysis .
After revision:  In this paper we overcome the difficulty by working with random locally convex modules endowed with the locally L^0 --convex conditional risk measures .