mathematics, a subadditive set function is a set function whose value, informally, has the property that the value of function on the union of two sets is at most...

subadditive set function. Let Ω {\displaystyle \Omega } be a set and f : 2 Ω → R {\displaystyle f\colon 2^{\Omega }\rightarrow \mathbb {R} } be a set...

mathematics Submodular set function – Set-to-real map with diminishing returns Subadditive set function τ-additivity ba space – The set of bounded charges...

In mathematics, subadditivity is a property of a function that states, roughly, that evaluating the function for the sum of two elements of the domain...

symmetric function if p ( − x ) = p ( x ) {\displaystyle p(-x)=p(x)} for all x ∈ X . {\displaystyle x\in X.} Every subadditive symmetric function is necessarily...

mathematics, especially measure theory, a set function is a function whose domain is a family of subsets of some given set and that (usually) takes its values...

x_{2}\})+f(X)} . A nonnegative submodular function is also a subadditive function, but a subadditive function need not be submodular. If Ω {\displaystyle...

A set function is called fractionally subadditive, or XOS (not to be confused with OXS), if it is the maximum of several non-negative additive set functions...

{\displaystyle u} is a subadditive set function. Assuming u ( ∅ ) {\displaystyle u(\emptyset )} is non-negative, every submodular function is subadditive. However,...

not contain i {\displaystyle i} . If v {\displaystyle v} is a subadditive set function, i.e., v ( S ⊔ T ) ≤ v ( S ) + v ( T ) {\displaystyle v(S\sqcup...

{x+y}{2}}\right)\geq {\frac {f(x)+f(y)}{2}}} If a function f is concave, and f(0) ≥ 0, then f is subadditive on [ 0 , ∞ ) {\displaystyle [0,\infty )} . Proof:...

operation and an order: Subadditive function: for which the value of f (x + y) is less than or equal to f (x) + f (y). Superadditive function: for which the value...

In mathematics, Kingman's subadditive ergodic theorem is one of several ergodic theorems. It can be seen as a generalization of Birkhoff's ergodic theorem...

require exponentially many queries). When agents' utilities are subadditive set functions (more general than submodular), a 1 m 1 / 2 − ϵ {\displaystyle...

superadditive integral Inner measure Subadditivity – Property of some mathematical functions Sublinear function – Type of function in linear algebra M. Marcus...

continuous functions. For a function between metric spaces, it is equivalent to admit a modulus of continuity that is either concave, or subadditive, or uniformly...

{1}{a}}|f(x)|\quad {\text{ for all }}x\in X.} The function p K {\textstyle p_{K}} has the following properties: It is subadditive: p K ( x + y ) ≤ p K ( x ) + p K (...

null sets is itself a null set (by countable subadditivity of μ {\displaystyle \mu } ). Any (measurable) subset of a null set is itself a null set (by...

combinations and point-wise limits of subadditive functions are subadditive, the Takagi function is subadditive for any value of the parameter w {\displaystyle...

with size n has a sum-free subset of size k. The function is subadditive, and by the Fekete subadditivity lemma, lim n f ( n ) n {\displaystyle \lim _{n}{\frac...

discrepancies and subadditive processes", Annals of Probability, 6 (1): 118–227, doi:10.1214/aop/1176995615, JSTOR 2242865. Origin of "Shattered sets" terminology...

In mathematics, the support function hA of a non-empty closed convex set A in R n {\displaystyle \mathbb {R} ^{n}} describes the (signed) distances of...

functions, and its dual is the homogeneous Lipschitz space of order n(1/p − 1). When p < 1, the Hp-quasinorm is not a norm, as it is not subadditive....

Let X {\displaystyle X} be a set and Σ {\displaystyle \Sigma } a σ-algebra over X . {\displaystyle X.} A set function μ {\displaystyle \mu } from Σ {\displaystyle...

is a continuous, nonincreasing function of the parameter α {\displaystyle \alpha } . A weak version of subadditivity can be proven: S α ( ρ A ) − S 0...

in a similar fashion for a function (see limit of a function). For a set, they are the infimum and supremum of the set's limit points, respectively....

In quantum information theory, strong subadditivity of quantum entropy (SSA) is the relation among the von Neumann entropies of various quantum subsystems...

processes such as the fractional Brownian motion. The Choquet integral, a subadditive or superadditive integral created by the French mathematician Gustave...

properties of entropy as a function of random variables (subadditivity and additivity), rather than the properties of entropy as a function of the probability...

measure theory, an outer measure or exterior measure is a function defined on all subsets of a given set with values in the extended real numbers satisfying...