Before revision: Equivalent characterizations of multi-portfolio time consistency are deduced for closed convex and coherent set-valued risk measures on L ^p_d(F_T ) with image space in the power set of L ^p_d(F_t ).
After revision: Equivalent characterizations of multi-portfolio time consistency are deduced for closed convex and coherent set-valued risk measures on L ^p_d(F_T ) with image space in the power set of L _d^p(\Omega,\mathcal F_t,\mathbb P ).