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.
After revision:  First, most of the principal results in the FKV paper were based on the premise that the locally L ^{0}--convex 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.