Definition:Infimum of Mapping/Real-Valued Function/Definition 1

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This page is about Infimum of Real-Valued Function. For other uses, see Infimum.

Definition

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

Let $f$ be bounded below on $S$.


The infimum of $f$ on $S$ is defined by:

$\displaystyle \inf_{x \mathop \in S} \map f x = \inf f \sqbrk S$

where

$\inf f \sqbrk S$ is the infimum in $\R$ of the image of $S$ under $f$.


Also see


Sources