- real-valued
function f {\displaystyle f} is
upper (respectively, lower)
semicontinuous at a
point x 0 {\displaystyle x_{0}} if,
roughly speaking, the function...
- \mathrm {d} x.} Then F {\displaystyle F} is
sequentially weakly lower semicontinuous on the L p {\displaystyle L^{p}}
space L p ( Ω ) {\displaystyle L^{p}(\Omega...
- can be
approximated in L1 from
above and
below by lower- and upper-
semicontinuous functions, respectively. It is
named after Giuseppe Vitali and Constantin...
- {\displaystyle X\times Y} with f ( ⋅ , y ) {\displaystyle f(\cdot ,y)}
upper semicontinuous and quasi-concave on X {\displaystyle X} , for
every fixed y ∈ Y {\displaystyle...
- A and B are
Hausdorff compact spaces, and K is an
upper semicontinuous or
lower semicontinuous function on A × B {\displaystyle A\times B} , then sup f...
-
topologically open. Sometimes, the
above continuity notions are
called semicontinuous, and a ⪰ {\displaystyle \succeq } is
called continuous if it is a closed...
- and
lower semicontinuous functions on R n . {\displaystyle \mathbb {R} ^{n}.} Then the
infimal convolution is
convex and
lower semicontinuous (but not...
-
arise when
working with
semicontinuous functions, in that a real-valued
function on a
topological space is
lower semicontinuous if and only if it is continuous...
- _{x\in K}f(x)} .
Slightly more generally, this is also true for an
upper semicontinuous function. (see
compact space#Functions and
compact spaces). We look...
- PMID 23767849. Wang, Qinbo; Cheng, Youwei; Wang, Lijun; Li, Xi (2007). "
Semicontinuous Studies on the
Reaction Mechanism and
Kinetics for the Liquid-Phase...
