subset C of a real or complex vector space is said to be absolutely convex or disked if it is convex and balanced (some people use the term "circled" instead...

a set of points is convex if it contains every line segment between two points in the set. Equivalently, a convex set or a convex region is a set that...

transformation of A {\displaystyle A} . Absolutely convex set – Convex and balanced set Absorbing set – Set that can be "inflated" to reach any point...

consisting of absolutely convex sets (that is, disks), where this neighborhood basis can further be chosen to also consist entirely of open sets or entirely...

1\right\}.} Conversely: Any locally convex topological vector space has a local basis consisting of absolutely convex sets. A common method to construct such...

Haar null set Convex set Balanced set, Absolutely convex set Fractal set Recursive set Recursively enumerable set Arithmetical set Diophantine set Hyperarithmetical...

D:={\textstyle \bigcap \limits _{|u|=1}}uW} will be convex and balanced (also known as an absolutely convex set or a disk) in addition to being absorbing in...

sublinear function. Absolutely convex set – Convex and balanced set Absorbing set – Set that can be "inflated" to reach any point Bounded set (topological vector...

symmetric sets. Any balanced subset of a real or complex vector space is symmetric. Absolutely convex set – Convex and balanced set Absorbing set – Set that...

vector spaces in a dual pair, as the polar set of a bounded set is an absolutely convex and absorbing set. The concept was first introduced by John von...

function does not have to be nonnegative-valued and also does not have to be absolutely homogeneous. Seminorms are themselves abstractions of the more well known...

an absolutely continuous and a singular continuous distribution, and thus any cumulative distribution function admits a decomposition as the convex sum...

mathematics, an infinite series of numbers is said to converge absolutely (or to be absolutely convergent) if the sum of the absolute values of the summands...

{\textstyle K} is convex then p K {\textstyle p_{K}} is subadditive. If K {\textstyle K} is balanced then p K {\textstyle p_{K}} is absolutely homogeneous;...

countable dimension then every string contains an absolutely convex string. Summative sequences of sets have the particularly nice property that they define...

instead of the sublinear property,R is convex, then R is a set-valued convex risk measure. A lower semi-continuous convex risk measure ϱ {\displaystyle \varrho...

continuous ⊂ absolutely continuous ⊂ uniformly continuous ⊂ continuous. Given two metric spaces (X, dX) and (Y, dY), where dX denotes the metric on the set X and...

region, is a convex set. More generally, one can show that when c=0, the interior of the region of absolute convergence is always a log-convex set in this...

monotonicity in a set of data Total monotonicity Cyclical monotonicity Operator monotone function Monotone set function Absolutely and completely monotonic...

is not locally convex: in ℓ p {\displaystyle \ell ^{p}} or L p ( [ 0 , 1 ] ) , {\displaystyle L^{p}([0,1]),} every open convex set containing the 0...

connected with convex sets: every seminorm is the Minkowski functional of some absorbing disk and, conversely, the Minkowski functional of any such set is a seminorm...

first-order condition for (1), which requires that the choice set X {\displaystyle X} have the convex and topological structure, and the objective function f...

of stochastic orders.[citation needed] Convex order is a special kind of variability order. Under the convex ordering, A {\displaystyle A} is less than...

In mathematics, the notions of an absolutely monotonic function and a completely monotonic function are two very closely related concepts. Both imply very...

Barry Convex, with his crew operating a dummy underneath the set. Lennick devised effects such as having the image of the Videodrome television set distort...

monotonicity. Gradients of convex functions are cyclically monotone. In fact, the converse is true. Suppose U {\displaystyle U} is convex and f : U ⇉ R n {\displaystyle...

is the Mackey topology, the topology of uniform convergence on all absolutely convex weakly compact subsets of X ′ {\displaystyle X'} . Given a dual pair...

described by specifying that an absolutely convex subset U of X is a neighborhood of 0 if and only if U ∩ Xi is an absolutely convex neighborhood of 0 in Xi for...

mathematics, a convex measure is a probability measure that — loosely put — does not assign more mass to any intermediate set "between" two measurable sets A and...

\infty ]=\mathbb {R} \cup \{\pm \infty \},} which appear in fields like convex analysis, the multiplication 0 ⋅ f ( x ) {\displaystyle 0\cdot f(x)} will...