The Santaló point of a function , and a functional form of Santaló inequality

@inproceedings{Artstein2004TheSP,
  title={The Santal{\'o} point of a function , and a functional form of Santal{\'o} inequality},
  author={S. Artstein and B. Klartag and Victor Milman},
  year={2004}
}
Let L(f) denotes the Legendre transform of a function f : R → R. We generalize a theorem of K. Ball about even functions, and prove that for any measurable function f ≥ 0, there exists a translation f̃(x) = f(x− a) such that ∫ 
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