Hypograph (mathematics)

In mathematics, the hypograph or subgraph of a function ${\displaystyle f:\mathbb {R} ^{n}\rightarrow \mathbb {R} }$ is the set of points lying on or below its graph. A related definition is that of such a function's epigraph, which is the set of points on or above the function's graph.

The domain (rather than the codomain) of the function is not particularly important for this definition; it can be an arbitrary set^[1] instead of ${\displaystyle \mathbb {R} ^{n}}$.