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