In mathematics, a superadditive set function is a set function whose value when applied to the union of two disjoint sets is greater than or equal to...

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...

In mathematics, a function f {\displaystyle f} is superadditive if f ( x + y ) ≥ f ( x ) + f ( y ) {\displaystyle f(x+y)\geq f(x)+f(y)} for all x {\displaystyle...

_{i}(v)\leq v(\{i\})} . Similarly, if v {\displaystyle v} is a superadditive set function, i.e., v ( S ⊔ T ) ≥ v ( S ) + v ( T ) {\displaystyle v(S\sqcup...

subadditive. The maximum of additive set functions is subadditive (dually, the minimum of additive functions is superadditive). Formally, for each i ∈ { 1 ,...

Pseudo-Boolean function Topkis's theorem Submodular set function Superadditive Utility functions on indivisible goods Topkis, Donald M., ed. (1998). Supermodularity...

functional – Function made from a set Norm (mathematics) – Length in a vector space Seminorm – Mathematical function Superadditivity – Property of a function Proofs...

u} is a superadditive set function. Assuming u ( ∅ ) {\displaystyle u(\emptyset )} is non-positive, every supermodular function is superadditive. However...

f} is a convex function of one real variable, and f ( 0 ) ≤ 0 {\displaystyle f(0)\leq 0} , then f {\displaystyle f} is superadditive on the positive...

fractionally-subadditive valuations. When agents' utilities are superadditive set functions (more general than supermodular), a ( log ⁡ m ) 1 + ϵ m {\displaystyle...

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 of...

grand coalition on smaller coalitions. Characteristic functions are often assumed to be superadditive (Owen 1995, p. 213). This means that the value of a...

solution Choquet integral – Subadditive or superadditive integral Superadditivity – Property of a function Triangle inequality – Property of geometry...

Recherche Scientifiques. Alzer, Horst (2009). "A superadditive property of Hadamard's gamma function". Abhandlungen aus dem Mathematischen Seminar der...

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....

A Choquet integral is a subadditive or superadditive integral created by the French mathematician Gustave Choquet in 1953. It was initially used in statistical...

fractional Brownian motion. The Choquet integral, a subadditive or superadditive integral created by the French mathematician Gustave Choquet in 1953...

E ) + g ( F ) {\displaystyle g(E\cup F)+g(E\cap F)\leq g(E)+g(F)} ; superadditive if for any E , F ∈ C {\displaystyle E,F\in {\mathcal {C}}} such that...

share is worth even more. On the contrary, when the valuations are only superadditive, PR still implies EF with two partners, but EF no longer implies PR...

_{i=1}^{n}A_{i}\right)\leq \sum _{i=1}^{n}\mu (A_{i}).} σ {\displaystyle \sigma } -Superadditivity: For any we A i ∈ A ( i = 1 , 2 , … )   {\displaystyle A_{i}\in {\mathcal...

is, φ ( ∅ ) = 0 {\displaystyle \varphi (\varnothing )=0} Superadditive: For any disjoint sets A {\displaystyle A} and B , {\displaystyle B,} φ ( A ∪ B...

of finitely presented groups. In particular, if f(n) ≥ n4 is a superadditive function whose binary representation is computable in time O ( f ( n ) 4...

share is worth even more. On the contrary, when the valuations are only superadditive, PR still implies EF with two partners, but EF no longer implies PR...

compared to the sum of each single modality together, an effect called the superadditive effect of multisensory integration. Neurons that respond to both visual...

expectations (previsions), aim to fill this gap. A lower probability function is superadditive but not necessarily additive, whereas an upper probability is...

subadditivity condition above is instead replaced by the condition: Superadditivity: for X , Y ∈ H {\displaystyle X,Y\in {\mathcal {H}}} then E [ X ] +...

Hu (2020) shows the endowment effect when the utility function is superadditive, i.e., the value of the whole is greater than the sum of its parts....

a subgroup that is not locally finite has superadditive distortion; conversely every superadditive function (up to asymptotic equivalence) can be found...

Lin, Minghua; Sra, Suvrit (2014). "Completely strong superadditivity of generalized matrix functions". arXiv:1410.1958 [math.FA]. Paksoy; Turkmen; Zhang...

Hence, every mFS-fair allocation is proportional. For every agent with superadditive utility, the MMSis worth at most 1 / n {\displaystyle 1/n} . Hence,...