Definition:Effective Domain/Convex Real-Valued Function/Real Vector Space

Definition

Let $\R^n$ be an $n$-dimensional real vector space.

Let $S \subseteq \R^n$ be a subset.

Let $f: S \to \overline \R$ be a convex function.

The effective domain of $f$ is:

$\Dom f := \set {x \in S : \map f x < + \infty }$

Sources

• 1970: Ralph Tyrell Rockafellar: Convex Analysis: $\S 4$: Convex Functions