Loterre: Mathématiques: hypograph

mathematical analysis > real analysis > hypograph

geometry > convex analysis > convex set > hypograph

hypograph

In mathematics, the hypograph or subgraph of a function ${\\displaystyle f:\\mathbb {R} ^{n}\ ightarrow \\mathbb {R} }$ 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 instead of ${\\displaystyle \\mathbb {R} ^{n}}$ .

(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Hypograph_(mathematics))

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