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Soit un Lagrangien {\cal L}(v,q) défini de V\times R^M dans R.
Le lemme de dualité faible affirme que:
\inf_q \sup_v {\cal L}(v,q) \geq \sup_q \inf_v{\cal L}(v,q)
\inf_v \sup_q {\cal L}(v,q) \leq \sup_q \inf_v{\cal L}(v,q)
\inf_v \sup_q {\cal L}(v,q) \geq \sup_v \inf_q{\cal L}(v,q)
\inf_v \sup_q {\cal L}(v,q) \geq \sup_q \inf_v{\cal L}(v,q)
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