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...

closed convex subset is strictly convex if and only if every one of its boundary points is an extreme point. A set C is absolutely convex if it is convex and...

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...

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

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

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...

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...

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

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

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

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...

{\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;...

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...

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...

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

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...

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...

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

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

ranked relative to each other but are not measured absolutely. Mode the most frequent value in the data set. This is the only central tendency measure that...

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

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...

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...

multiplication means that for every absolutely convex neighborhood V {\displaystyle V} of zero, there is an absolutely convex neighborhood U {\displaystyle...

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...

locally convex because the set of all open balls centered at the origin forms a neighbourhood basis at the origin consisting of convex balanced open sets. This...