mathematics, an additive set function is a function mapping sets to numbers, with the property that its value on a union of two disjoint sets equals the sum...

or results of a statistical trial or experiment Sigma-additive set function – Mapping function Sigma-ring – Ring closed under countable unions "11. Measurable...

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

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...

Harish-Chandra's σ function Weierstrass sigma function Sigma additivity Sigma (album) Sigma (DJs), a British drum and bass duo Sigma AZ (band), punk rock...

may appear reasonable. However the closest generalization to mass is sigma additivity, which gives rise to the Lebesgue measure. It assigns a measure of...

form of its probability density function is f ( x ) = 1 σ 2 π e − 1 2 ( x − μ σ ) 2 {\displaystyle f(x)={\frac {1}{\sigma {\sqrt {2\pi }}}}e^{-{\frac {1}{2}}\left({\frac...

is no prime number that divides both of them. Then an arithmetic function a is additive if a(mn) = a(m) + a(n) for all coprime natural numbers m and n;...

addition operation Additive set-function see Sigma additivity Additive category, a preadditive category with finite biproducts Additive inverse, an arithmetic...

In statistics, an additive model (AM) is a nonparametric regression method. It was suggested by Jerome H. Friedman and Werner Stuetzle (1981) and is an...

Delta-sigma (ΔΣ; or sigma-delta, ΣΔ) modulation is an oversampling method for encoding signals into low bit depth digital signals at a very high sample-frequency...

{y-\mu }{\sigma }}} . Other definitions of the Q-function, all of which are simple transformations of the normal cumulative distribution function, are also...

generalized additive model (GAM) is a generalized linear model in which the linear response variable depends linearly on unknown smooth functions of some...

field of measure theory, τ-additivity is a certain property of measures on topological spaces. A measure or set function μ {\displaystyle \mu } on a...

In economics, additive utility is a cardinal utility function with the sigma additivity property.: 287–288  Additivity (also called linearity or modularity)...

E\in \Sigma } Definition 1.3. The variation (also called absolute variation) of the signed measure μ {\displaystyle \mu } is the set function | μ | (...

{B(\alpha _{t}+i\sigma _{t}u,\beta _{t}-i\sigma u)}{B(\alpha _{t},\beta _{t})}}\right)^{\delta _{t}}e^{i\mu _{t}u}\;\;.} Two subcases of additive logistic process...

dual: the additive form. If Y is reproductive, then Z = λ Y {\displaystyle Z=\lambda Y} with λ = 1 σ 2 {\displaystyle \lambda ={\frac {1}{\sigma ^{2}}}}...

γ(n) = (−1)ω(n), where the additive function ω(n) is the number of distinct primes dividing n. τ(n): the Ramanujan tau function. All Dirichlet characters...

club set stratified A formula of set theory is stratified if and only if there is a function σ {\displaystyle \sigma } which sends each variable appearing...

{\displaystyle ba(\Sigma )} of an algebra of sets Σ {\displaystyle \Sigma } is the Banach space consisting of all bounded and finitely additive signed measures...

_{i}f(X_{i})} . The set of fractionally subadditive functions equals the set of functions that can be expressed as the maximum of additive functions, as in the...

processing and statistics, a window function (also known as an apodization function or tapering function) is a mathematical function that is zero-valued outside...

\sigma {\sqrt {2\ \pi \ }}\ }}\exp \left(-{\frac {\ (\ln x-\mu )^{2}\ }{2\ \sigma ^{2}}}\right)~.\end{aligned}}} The cumulative distribution function is...

set algebra 𝜎-ring – Ring closed under countable unions Sigma additivity – Mapping functionPages displaying short descriptions of redirect targets Bauer...

particularly norms and square roots. Additive maps are special cases of subadditive functions. A subadditive function is a function f : A → B {\displaystyle f\colon...

not a result. A cylinder set measure can be intuitively understood as defining a finitely additive function on the cylinder sets of the topological vector...

which the additive monoid is a complete monoid, meaning that it has an infinitary sum operation Σ I {\displaystyle \Sigma _{I}} for any index set I {\displaystyle...

which are sigma-additive set functions. However, the Type I integral is not multiplicative as a functional. Given two product-integrable functions f , g {\displaystyle...

In mathematics, a nonempty collection of sets is called a 𝜎-ring (pronounced sigma-ring) if it is closed under countable union and relative complementation...