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