Lower hemicontinuity

Definition

Given $A \in \mathbb{R}^n$ and compact set $Y \in \mathbb{R}^k$, the correspondence $f: A \to Y$ is l.h.c. if for every sequence $x_m \to x \in A$ with $x^m \in A$ for all $m$, and every $y \in f(x)$, we can find a sequence $y^m \to y$.

Notes

lower semicontinuity is a more general form

See also

• Upper hemicontinuity