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A remarkable theorem of Mazur and Orlicz which generalizes the Hahn-Banach theorem is here put in a convenient form through an equality which will be referred to as the Mazur-Orlicz equality. Applications of the Mazur-Orlicz equality to lower barycenters for means, separation principles, Lax-Milgram lemma in reflexive Banach spaces, and monotone variational inequalities are provided.
Dans cete note, nous présentons un théorème de minimax (Théorème A) formulé seulement en langage de la théorie des ensembles. Ce résultat permet de déduire de façon immédiate (en utilisant un lemme de topologie générale) plusieurs théorèmes de minimax bien connus.
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