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 the sum of values of the function applied to each of the sets separately. This definition is analogous to the notion of superadditivity for real-valued functions. It is contrasted to subadditive set function.
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mathematics, especially measure theory, a setfunction is a function whose domain is a family of subsets of some given set and that (usually) takes its values...
subadditive. The maximum of additive setfunctions is subadditive (dually, the minimum of additive functions is superadditive). Formally, for each i ∈ { 1 ,...
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...
_{i}(v)\leq v(\{i\})} . Similarly, if v {\displaystyle v} is a superadditivesetfunction, i.e., v ( S ⊔ T ) ≥ v ( S ) + v ( T ) {\displaystyle v(S\sqcup...
u} is a superadditivesetfunction. Assuming u ( ∅ ) {\displaystyle u(\emptyset )} is non-positive, every supermodular function is superadditive. However...
fractionally-subadditive valuations. When agents' utilities are superadditivesetfunctions (more general than supermodular), a ( log m ) 1 + ϵ m {\displaystyle...
finally verify that f is subadditive. The negative of a subadditive function is superadditive. Entropy plays a fundamental role in information theory and statistical...
Recherche Scientifiques. Alzer, Horst (2009). "A superadditive property of Hadamard's gamma function". Abhandlungen aus dem Mathematischen Seminar der...
grand coalition on smaller coalitions. Characteristic functions are often assumed to be superadditive (Owen 1995, p. 213). This means that the value of a...
Pseudo-Boolean function Topkis's theorem Submodular setfunctionSuperadditive Utility functions on indivisible goods The equivalence between the definition...
an order: Subadditive function: for which the value of f (x + y) is less than or equal to f (x) + f (y). Superadditivefunction: for which the value of...
absolutely homogenousPages displaying wikidata descriptions as a fallback Superadditivity Proofs Let x ∈ X . {\displaystyle x\in X.} The triangle inequality...
fractional Brownian motion. The Choquet integral, a subadditive or superadditive integral created by the French mathematician Gustave Choquet in 1953...
is, φ ( ∅ ) = 0 {\displaystyle \varphi (\varnothing )=0} Superadditive: For any disjoint sets A {\displaystyle A} and B , {\displaystyle B,} φ ( A ∪ B...
A Choquet integral is a subadditive or superadditive integral created by the French mathematician Gustave Choquet in 1953. It was initially used in statistical...
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....
of finitely presented groups. In particular, if f(n) ≥ n4 is a superadditivefunction whose binary representation is computable in time O ( f ( n ) 4...
a subgroup that is not locally finite has superadditive distortion; conversely every superadditivefunction (up to asymptotic equivalence) can be found...
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...
Hence, every mFS-fair allocation is proportional. For every agent with superadditive utility, the MMSis worth at most 1 / n {\displaystyle 1/n} . Hence,...
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...
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 ] +...
additive positive utilities, but also for any superadditive utilities, whether positive or negative: For superadditive utilities, there is a polynomial-time algorithm...
compared to the sum of each single modality together, an effect called the superadditive effect of multisensory integration. Neurons that respond to both visual...
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