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In [[economics]], '''additive utility''' is a [[cardinal utility]] function with the [[sigma additivity]] |+Additive utility ...

{{About||additive functions in number theory|Additive function|additive functions on the reals|Cauchy's functional equation}} ...ra|algebra]], an '''additive map''', '''<math>Z</math>-linear map''' or '''additive function''' is a [[Function (mathematics)|function]] <math>f</math> that pr ...

{{About|the statistical method|additive color models|Additive color}} In [[statistics]], an '''additive model''' ('''AM''') is a [[nonparametric regression]] method. It was sugges ...

...s is thematically related to the [[subadditivity]] property of real-valued functions. ...here <math>2^\Omega</math> denotes the [[Power set#Representing subsets as functions|power set]] of <math>\Omega</math>. The function ''f'' is ''subadditive'' i ...

...ssignment valuation|OXS]]), if it is the maximum of several non-negative [[additive set function]]s. ...ite journal|doi=10.1137/070680977|title=On Maximizing Welfare when Utility Functions Are Subadditive|journal=SIAM Journal on Computing|volume=39|pages=122–142|y ...

...223}}</ref> Specifically, if one considers [[AdaBoost]] as a [[generalized additive model]] and then applies the cost function of [[logistic regression]], one ...be seen as a [[convex optimization]]. Specifically, given that we seek an additive model of the form ...

In [[statistics]], a '''functional additive model''' ('''FAM''') can be viewed as an extension of a [[generalized funct ===Functional Additive Model=== ...

...']] and the transition probability to a state at the next time is a sum of functions, each depending on the next state and one of the ''m'' previous states. ...rder ''m''), and the influence of previous variables on a generated one is additive, ...

...finition is analogous to the notion of [[superadditivity]] for real-valued functions. It is contrasted to [[subadditive set function]]. ...ditiveX.pdf | title=ON FINDING ADDITIVE, SUPERADDITIVE AND SUBADDITIVE SET-FUNCTIONS SUBJECT TO LINEAR INEQUALITIES | date=1988 | accessdate=21 December 2015 | ...

...Dynamical generalizations of the prime number theorem and disjointness of additive and multiplicative semigroup actions | title = On some arithmetical functions ...

=== Additive utility (AU) === The AU extension is based on the notion of an [[additive utility]] function. ...

...s from a set <math>A</math> is written <math>u(A)</math>. Cardinal utility functions are often normalized such that <math>u(\emptyset)=0</math>, where <math>\em ...> and <math>u(A)\geq u(B)</math> implies <math>A \succeq B</math>. Utility functions can have several properties.<ref name=gs99>{{Cite journal | doi = 10.1006/j ...

==Definitions of additive elliptic hypergeometric series== The additive elliptic shifted factorials are defined by ...

...hematics)|function]] <math>f:G\to\mathbb{R}</math> which is [[additive map|additive]] up to bounded error, i.e. there exists a [[Constant (mathematics)|constan ...f a group homomorphism and a bounded function is also a quasimorphism, and functions of this form are sometimes referred to as "trivial" quasimorphisms.<ref>Fri ...

...unction. The article [[ordinal utility]] describes some properties of such functions and some ways by which they can be calculated. ...nted by a numeric function. Such functions are called [[cardinal utility]] functions. The article [[Von Neumann–Morgenstern utility theorem]] describes some way ...

...orem''' is an [[existence theorem]] concerning economical [[additive basis|additive bases]] of every order. More specifically, it states that for every fixed i ...sometimes ''thin''<ref>As in Tao & Vu (2006), p. 13.</ref>) when it is an additive basis of order ''h'' and ...

...eorem in probabilistic number theory on additive complex-valued arithmetic functions}} Suppose ''f'' is an [[Additive function|additive]] complex-valued [[arithmetic function]], and write ''p'' for an arbitrary ...

..., then the duality functor is given by the duality of the Hopf algebras of functions. ...iequivalence with commutative affine [[formal group]]s, so if ''G'' is the additive group <math>\mathbf{G'}_a</math>, then its Cartier dual is the multiplicati ...

==Application to maximal functions and maximal inequalities== ...al form of the covering principle and relative differentiation of additive functions, I|journal=[[Mathematical Proceedings of the Cambridge Philosophical Societ ...

...d]] with a further unary operation that is a homomorphism from the field's additive group to its multiplicative group. This generalizes the usual idea of [[ex ...Thus an exponential function on a field is a [[homomorphism]] between the additive group of ''F'' and its multiplicative group. ...