Epigraph (mathematics)

Epigraph (mathematics)

In mathematics, the epigraph of a function f : Rn→R is the set of points lying on or above its graph:

and the strict epigraph of the function is:

The same definitions are valid for a function that takes values in R ∪ ∞. In this case, the epigraph is empty if and only if f is identically equal to infinity.

Similarly, the set of points on or below the function is its hypograph.