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Hahn's contributions to mathematics include the famous Hahn-Banach theorem and (independently of Banach and Steinhaus) the uniform boundedness principle. Other theorems are the Hahn decomposition theorem, the Vitali-Hahn-Saks theorem, the Hahn-Mazurkiewicz theorem and the Hahn embedding theoremIn mathematics, the Hahn embedding theorem states that every totally ordered abelian group can be embedded as a subgroup of the additive group of a real closed field. It is therefore a generalization of Holder's theorem. Order theory Abelian group theory.