▾ Set of symbols
▾ Alphabet
▾ Deduction system
▾ Theory
▾ Zermelo-Fraenkel set theory
▾ Set
▾ Binary cartesian set product
▾ Binary relation
▾ Map
▾ Map inverse image
▾ Level set
Sublevel set
Formulation 0
Let $P = (Y, {\leq})$ be a D1103: Partially ordered set.
Let $f : X \to Y$ be a D18: Map.
The sublevel set of $f$ with respect to $y \in Y$ and $P$ is the D11: Set \begin{equation} \{ f \leq y \} : = \{ x \in X : f(x) \leq y \} \end{equation}
Also known as
Lower Contour set, Lower level set
Child definitions
» D2951: Strict sublevel set
Results
» R3532: Tautological pointwise lower bound from indicator function on sublevel set
» R3529: Tautological pointwise inequality from indicator functions on sublevel sets
» R2182: Isotonicity of real sublevel sets
» R4182: Isotonicity of sublevel probabilities for a random real number