Definition:Bounded Mapping/Real-Valued/Definition 3

This page is about Bounded in the context of Real-Valued Function. For other uses, see Bounded.

Definition

Let $f: S \to \R$ be a real-valued function.

$f$ is bounded on $S$ if and only if:

$\exists a, b \in \R_{\ge 0}: \forall x \in S: \map f x \in \closedint a b$

where $\closedint a b$ denotes the (closed) real interval from $a$ to $b$.

Also see

• Equivalence of Definitions of Bounded Real-Valued Function

• Definition:Bound of Real-Valued Function

Sources

• 1970: Arne Broman: Introduction to Partial Differential Equations ... (previous) ... (next): Chapter $1$: Fourier Series: $1.1$ Basic Concepts: $1.1.2$ Definitions