The concept of duality in convex analysis , and the characterization of the Legendre transform

@inproceedings{ArtsteinAvidan2009TheCO,
  title={The concept of duality in convex analysis , and the characterization of the Legendre transform},
  author={Shiri Artstein-Avidan and V. D. Milman},
  year={2009}
}
In the main theorem of this paper we show that any involution on the class of lower semi-continuous convex functions which is order-reversing, must be, up to linear terms, the well known Legendre transform. 
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