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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
Superadditive_set_function
Function from sets to numbers
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
Set_function
Property of a function
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
Superadditivity
Concept in game theory
_{i}(v)\leq v(\{i\})} . Similarly, if v {\displaystyle v} is a superadditive set function, i.e., if v ( S ∪ T ) ≥ v ( S ) + v ( T ) {\displaystyle v(S\cup
Shapley_value
subadditive. The maximum of additive set functions is subadditive (dually, the minimum of additive functions is superadditive). Formally, for each i ∈ { 1 ,
Subadditive_set_function
Lemma concerning the limit of subadditive sequences
{ a n } n = 1 ∞ {\displaystyle \{a_{n}\}_{n=1}^{\infty }} is called superadditive if and only if for all m , n ∈ N {\displaystyle m,n\in \mathbb {N} }
Fekete's_lemma
Class of mathematical functions
Pseudo-Boolean function Topkis's theorem Submodular set function Superadditive Utility functions on indivisible goods Topkis, Donald M., ed. (1998). Supermodularity
Supermodular_function
Type of function in linear algebra
functional – Function made from a set Norm (mathematics) – Length in a vector space Seminorm – Mathematical function Superadditivity – Property of a function Proofs
Sublinear_function
Real function with secant line between points above the graph itself
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
Convex_function
u} is a superadditive set function. Assuming u ( ∅ ) {\displaystyle u(\emptyset )} is non-positive, every supermodular function is superadditive. However
Utility functions on indivisible goods
Utility_functions_on_indivisible_goods
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
List_of_types_of_functions
fractionally-subadditive valuations. When agents' utilities are superadditive set functions (more general than supermodular), a ( log m ) 1 + ϵ m {\displaystyle
Welfare_maximization
Property of some mathematical functions
solution Choquet integral – Subadditive or superadditive integral Superadditivity – Property of a function Triangle inequality – Property of geometry
Subadditivity
Game where groups of players may enforce cooperative behaviour
grand coalition on smaller coalitions. Characteristic functions are often assumed to be superadditive (Owen 1995, p. 213). This means that the value of a
Cooperative_game_theory
Generalization of a measure
_{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
Content_(measure_theory)
Bounds of a sequence
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.
Limit inferior and limit superior
Limit_inferior_and_limit_superior
Product of numbers from 1 to n
Recherche Scientifiques. Alzer, Horst (2009). "A superadditive property of Hadamard's gamma function". Abhandlungen aus dem Mathematischen Seminar der
Factorial
Subadditive or superadditive integral
A Choquet integral is a subadditive or superadditive integral created by the French mathematician Gustave Choquet in 1953. It was initially used in statistical
Choquet_integral
Group theory function
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
Dehn_function
Operation in mathematical calculus
subadditive or superadditive integral created by Gustave Choquet in 1953. The Bochner integral, a generalization of the Lebesgue integral to functions that take
Integral
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
Proportional_division
is, φ ( ∅ ) = 0 {\displaystyle \varphi (\varnothing )=0} Superadditive: For any disjoint sets A {\displaystyle A} and B , {\displaystyle B,} φ ( A ∪ B
Inner_measure
Theory of generalized measures in mathematics
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
Fuzzy_measure_theory
Physiological capacity
compared to the sum of each single modality together, an effect called the superadditive effect of multisensory integration. Neurons that respond to both visual
Sense
Probability theory for low quality data
expectations (previsions), aim to fill this gap. A lower probability function is superadditive but not necessarily additive, whereas an upper probability is
Imprecise_probability
Criterion for fair division
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
Envy-freeness
subadditivity condition above is instead replaced by the condition: Superadditivity: for X , Y ∈ H {\displaystyle X,Y\in {\mathcal {H}}} then E [ X ] +
Nonlinear_expectation
Cognitive bias
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.
Endowment_effect
Concept in geometric group theory
a subgroup that is not locally finite has superadditive distortion; conversely every superadditive function (up to asymptotic equivalence) can be found
Subgroup_distortion
In mathematics, invariant of square matrices
Lin, Minghua; Sra, Suvrit (2014). "Completely strong superadditivity of generalized matrix functions". arXiv:1410.1958 [math.FA]. Paksoy; Turkmen; Zhang
Determinant
Fair division problem for discrete items
Hence, every mFS-fair allocation is proportional. For every agent with superadditive utility, the MMSis worth at most 1 / n {\displaystyle 1/n} . Hence,
Fair_item_allocation
additive positive utilities, but also for any superadditive utilities, whether positive or negative: For superadditive utilities, there is a polynomial-time algorithm
Fair allocation of items and money
Fair_allocation_of_items_and_money
Ecological mechanism enabling species to coexist
competition on fitness does not change with the environment. If γ > 0 (superadditivity), it means that the adverse effects of competition during a bad year
Storage_effect
SUPERADDITIVE SET-FUNCTION
SUPERADDITIVE SET-FUNCTION
Female
Egyptian
, a sister of Sekherta.
Surname or Lastname
English and German
English and German : topographic name for someone who lived by the sea-shore or beside a lake, from Middle English see ‘sea’, ‘lake’ (Old English sǣ), Middle High German sē. Alternatively, the English name may denote someone who lived by a watercourse, from an Old English sēoh ‘watercourse’, ‘drain’.
Female
Egyptian
, the wife of Osirtesen.
Female
Egyptian
, a sister of Sekherta.
Male
English
Short form of English Stephen, STE means "crown."
Female
Egyptian
, a wife and daughter of Antef.
Female
Egyptian
, an uncertain goddess.
Male
Hindi/Indian
(सेठ) Hindi name derived from the Sanskrit word setu, SETH means "bridge." Compare with other forms of Seth.
Male
English
Anglicized form of Hebrew Sheth, SETH means "buttocks." In the bible, this is the name of the third son of Adam and Eve. Compare with other forms of Seth.
Boy/Male
Egyptian Hebrew Swedish
Son of Seb and Nut.
Female
English
Short form of English Elizabeth, BET means "God is my oath."Â
Surname or Lastname
English
English : variant spelling of See.
Male
Egyptian
, the seven great spirits of the Ritual of the Dead.
Female
Egyptian
, second wife of Antef.
Surname or Lastname
English
English : perhaps a variant of Sait, from the Old English personal name Sǣgēat (‘sea Geat’).
Female
Hungarian
Hungarian form of Greek Elisabet, ERZSÉBET means "God is my oath."
Male
Hebrew
Variant spelling of Hebrew Sheth, SHET means "buttocks."
Female
Egyptian
, the mother of Fai-hor-ou-oer.
Male
Egyptian
, the seven great spirits of the Ritual of the Dead.
Female
Egyptian
, the wife of the usurper Sipthah.
SUPERADDITIVE SET-FUNCTION
SUPERADDITIVE SET-FUNCTION
Boy/Male
Australian, Polish
Born to Nobility; High-born; Well-born
Boy/Male
Sikh
Lord of lords
Boy/Male
Indian, Punjabi, Sikh
Lamp of Art
Girl/Female
Latin
Prudent.
Boy/Male
Muslim
Fortunate, Happy, Lucky
Girl/Female
Hindu, Indian, Marathi
Pure Like a Moon; Full Moon
Boy/Male
Hindu, Indian
Female Mountain Goat
Boy/Male
Indian, Sanskrit
Without Weakness
Boy/Male
Hindu
Radiant Prince
Boy/Male
Muslim
The white falcon, King
SUPERADDITIVE SET-FUNCTION
SUPERADDITIVE SET-FUNCTION
SUPERADDITIVE SET-FUNCTION
SUPERADDITIVE SET-FUNCTION
SUPERADDITIVE SET-FUNCTION
a.
Firm; unchanging; obstinate; as, set opinions or prejudices.
v. t.
To cause to sit; to make to assume a specified position or attitude; to give site or place to; to place; to put; to fix; as, to set a house on a stone foundation; to set a book on a shelf; to set a dish on a table; to set a chest or trunk on its bottom or on end.
n.
Direction or course; as, the set of the wind, or of a current.
n.
That which is set, placed, or fixed.
a.
Regular; uniform; formal; as, a set discourse; a set battle.
n.
A young plant for growth; as, a set of white thorn.
a.
Established; prescribed; as, set forms of prayer.
v. i.
To fit or suit one; to sit; as, the coat sets well.
v. t.
To compose; to arrange in words, lines, etc.; as, to set type; to set a page.
v. t.
To make to agree with some standard; as, to set a watch or a clock.
v. t.
To reduce from a dislocated or fractured state; to replace; as, to set a broken bone.
imp. & p. p.
of Set
n.
The act of adding something in excess or something extraneous; also, something which is added in excess or extraneously.
v. t.
To put in order in a particular manner; to prepare; as, to set (that is, to hone) a razor; to set a saw.
n.
See Set, n., 2 (e) and 3.
v. t.
To establish as a rule; to furnish; to prescribe; to assign; as, to set an example; to set lessons to be learned.
v. i.
To be fixed for growth; to strike root; to begin to germinate or form; as, cuttings set well; the fruit has set well (i. e., not blasted in the blossom).
v. t.
To determine; to appoint; to assign; to fix; as, to set a time for a meeting; to set a price on a horse.
a.
Fixed in position; immovable; rigid; as, a set line; a set countenance.
n.
A series of as many games as may be necessary to enable one side to win six. If at the end of the tenth game the score is a tie, the set is usually called a deuce set, and decided by an application of the rules for playing off deuce in a game. See Deuce.