In the dual $L^{Phi^*}$ of a $Delta_2$-Orlicz space $L^Phi$, we show thata proper (resp. finite) convex function is lower semicontinuous (resp.continuous) for the Mackey topology $au(L^{Phi^*},L^Phi)$ if and only if oneach order interval $[-zeta,zeta]={xi: -zetaleq xileqzeta}$($zetain L^{Phi^*}$), it is lower semicontinuous (resp. continuous) for thetopology of convergence in probability. For this purpose, we provide thefollowing Koml'os type result: every norm bounded sequence $(xi_n)_n$ in$L^{Phi^*}$ admits a sequence of forward convex combinations$ar{xi}_ninmathrm{conv}(xi_n,xi_{n+1},...)$ such that$sup_n|ar{xi}_n|in L^{Phi^*}$ and $ar{xi}_n$ converges a.s.
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机译：在$ delta_2 $ -ORLICZ SPACE $ L ^ PHI $的双重$ l ^ { phi ^ *}。我们显示适当的（resp。有限）凸起功能是较低的半连续（RESP.CONTINUUL） mackey拓扑$ tau（l ^ { phi ^ *}，l ^ phi）$如果any oneach订单间隔$ [ - zeta， zeta] = { xi： - zeta leq xi $（$ zeta in l ^ { phi ^ *} $），它是较低的半连续（连续），用于概率收敛性。为此目的，我们提供了关注的Koml 'OS类型结果：每种常态序列$（ xi_n）_n $ in $ l ^ { phi ^ *} $概述一系列前进凸组合$ bar { xi} _n in mathrm {conv}（ xi_n， xi_ {n + 1}，......）$，使得$ sup_n | bar { xi} _n | 在l ^ { phi ^ *} $和$ bar { xi} _n $收敛为
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