What is "hypograph"

n. (context mathematics of a function English) the set of all points lying on or below its graph.

In mathematics, the hypograph or subgraph of a function f : R → R is the set of points lying on or below its graph:

hypf = {(x, μ)  :  x ∈ R,  μ ∈ R,  μ ≤ f(x)} ⊆ R

and the strict hypograph of the function is:

hypf = {(x, μ)  :  x ∈ R,  μ ∈ R,  μ < f(x)} ⊆ R.

The set is empty if f ≡  − ∞.

The domain (rather than the co-domain) of the function is not particularly important for this definition; it can be an arbitrary set instead of R.

Similarly, the set of points on or above the function's graph is its epigraph.

The term “hypograph” may refer to

• the hypograph of a mathematical function — the set of points lying on or below its graph.