epigraph (mathematics)

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

The strict epigraph is the epigraph with the graph itself removed:

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.