- set-valued functions. A set-valued
function that is both
upper and
lower hemicontinuous is said to be
continuous in an
analogy to the
property of the same name...
- )\}} . If C {\displaystyle C} is
continuous (i.e. both
upper and
lower hemicontinuous) at θ {\displaystyle \theta } , then the
value function f ∗ {\displaystyle...
- and
convex subset of some
Euclidean space Rn. Let φ: S→2S be an
upper hemicontinuous set-valued
function on S with the
property that φ(x) is non-empty, closed...
- many
other properties loosely ****ociated with
approximability of
upper hemicontinuous multifunctions via
continuous functions explains why
upper hemicontinuity...
-
Banach space. Let F : X → Y {\displaystyle F\colon X\to Y} be a
lower hemicontinuous set-valued
function with
nonempty convex closed values. Then
there exists...
- r(\sigma )} is nonempty. r ( σ ) {\displaystyle r(\sigma )} is
upper hemicontinuous r ( σ ) {\displaystyle r(\sigma )} is convex.
Condition 1. is satisfied...
- selection: X is a
paracompact space; Y is a
Banach space; F is
lower hemicontinuous; for all x in X, the set F(x) is nonempty,
convex and closed. The approximate...
- ( p ) {\displaystyle {\tilde {S}}^{j}(p)} has
closed graph ("upper
hemicontinuous") ⟨ p , Z ~ ( p ) ⟩ ≤ 0 {\displaystyle \langle p,{\tilde {Z}}(p)\rangle...
- {\displaystyle F:X\to 2^{Y}} has a
closed graph if and only if it is
upper hemicontinuous and F(x) is a
closed set for all x ∈ X {\displaystyle x\in X} . If T...
-
bounded set.
Existence theory usually ****umes that F(t, x) is an
upper hemicontinuous function of x,
measurable in t, and that F(t, x) is a closed, convex...
