Fenchel-Moreau theorem
= Fenchel-Moreau theorem
{c}
{title2=$J^{**}=J$}
A proper lower-semicontinuous convex functional on a real <Banach space> equals its biconjugate, with the canonical embedding in the bidual understood. One inequality follows from the <Fenchel–Young inequality>; separation of a point below the closed convex epigraph gives the opposite inequality. This is the closed-convex analogue of recovering a function from all its affine supporting functions.