Before revision:  First, most of the principal results in the FKV paper were based on the premise that the locally L ^{0}--convex topology for every locally L ^{0--conditional risk measure (1\leq p\leq+\infty) can be uniquely extended to an L^{0}} --convex module may be induced by a family of L^{0 the FKV paper ever gave a proof of this premise, but there was a hole in this proof, in fact, it remains open up to now whether the premise is valid or not. 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.
After revision:  First, most of the principal results in the FKV paper were based on the premise that the locally L ^{0}--convex topology for every locally L ^{0--conditional risk measure (1\leq p\leq+\infty) can be uniquely extended to an L^{0}} --convex module may be induced by a family of L^{0 the process we find that combining the countable concatenation hull of a set and the local property of conditional risk measures is a very useful analytic skill that may considerably simplify and improve the study of L^{0 --convex topology rather than locally L^0--convex modules.