Before revision:  For this purpose, we provide the following Koml\'os type result: every norm bounded sequence (\xi_n)_n in L ^{\Phi^* admits a sequence of forward convex combinations  \bar _n\inconv(\xi_n,n+1,...) such that \sup_n|  \bar _n|\in L ^{\Phi^* and }  and }\bar _n converges a.s.
After revision:  For this purpose, we provide the following Koml\'os type result: every norm bounded sequence (\xi_n)_n in L _{\Phi^* admits a sequence of forward convex combinations  \bar _n\inconv(\xi_n,n+1,...) such that \sup_n|  \bar _n|\in L ^{\Phi^* and } and }\bar _n converges a.s.