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Longer titles found: Weakly measurable function (view), Strongly measurable function (view), Bochner measurable function (view)

searching for Measurable function 54 found (195 total)

alternate case: measurable function

Measurable Riemann mapping theorem (319 words) [view diff] exact match in snippet view article find links to article

equations. The theorem of Ahlfors and Bers states that if μ is a bounded measurable function on C with ‖ μ ‖ ∞ < 1 {\displaystyle \|\mu \|_{\infty }<1} , then

P)} is assumed to be complete (otherwise it cannot be standard). A measurable function f : Ω → R {\displaystyle \textstyle f:\Omega \to \mathbb {R} } induces

locally integrable and does not change sign in Ω, and there is a measurable function K(x) ≥ 1 such that | D f ( x ) | 2 ≤ K ( x ) | J ( x , f ) | {\displaystyle

[0,\infty ),B\in {\mathcal {E}}^{*}\right\}.} For each Borel measurable function f {\displaystyle f} on E {\displaystyle E} , define, for each x ∈

which extends a Riemann-type construction for the integral of a measurable function both to higher-dimensional domains and, in the case of one dimension

{\mathcal {F}},P)} . Suppose that f {\displaystyle f} is a Borel measurable function of the real line into [0,∞]. Then the following three assertions

])}{2\varepsilon }}=1} (where μ denotes Lebesgue measure). A Lebesgue-measurable function g : E → R is said to have approximate limit y at x (a point of density

of the pool will only depend on the particle itself. Consider a measurable function σ : R d × P ( R d ) → M d ( R ) {\displaystyle \sigma :\mathbb {R}

statistics, a graphon (also known as a graph limit) is a symmetric measurable function W : [ 0 , 1 ] 2 → [ 0 , 1 ] {\displaystyle W:[0,1]^{2}\to [0,1]}

\mu } -almost everywhere. In that case, the essential support of a measurable function f : X → R {\displaystyle f:X\to \mathbb {R} } written e s s s u p

ρ(φ(E)) = 0 whenever μ(E) = 0). Then there exists a real-valued Borel measurable function w on X such that for every Lebesgue integrable function f : Y → R

makes Hp into a complete metric space. When 0 < p ≤ 1, a bounded measurable function f of compact support is in the Hardy space Hp if and only if all

\mathbb {R} ^{k}} , k ∈ N {\displaystyle k\in \mathbb {N} } , is any measurable function. Let ( Ω , F , P ) {\displaystyle (\Omega ,{\mathcal {F}},\mathbb

{\displaystyle w\colon \Omega \to \mathbb {R} ^{+}} is a non-negative measurable function. In this context, the weight function w ( x ) {\displaystyle w(x)}

{\mathcal {B}})} be a measurable space. If T {\displaystyle T} is a measurable function from X {\displaystyle X} to itself and μ {\displaystyle \mu } a probability

{\displaystyle f^{*}} the symmetric decreasing rearrangement of nonnegative measurable function f and define it as f ∗ ( x ) := ∫ 0 ∞ 1 { y : f ( y ) > t } ∗ ( x

_{s})K(ds)\right\}} where α N {\displaystyle \alpha _{N}} is a positive measurable function and K {\displaystyle K} is a continuous functional of ξ {\displaystyle

stopped at τk is a martingale. Let Wt be the Wiener process and ƒ a measurable function such that E ⁡ | f ( W 1 ) | < ∞ . {\displaystyle \operatorname {E}

{\displaystyle f:\Omega \to \mathbb {R} } be a μ {\displaystyle \mu } -measurable function and φ : R → R {\displaystyle \varphi :\mathbb {R} \to \mathbb {R}

model is differentiable in quadratic mean. That is, there exists a measurable function f : X → R k {\displaystyle f:{\mathcal {X}}\rightarrow \mathbb {R}

A({\mathit {G}})} . The generalized Bochner theorem states that a measurable function on G {\displaystyle {\mathit {G}}} is equal, almost everywhere, to

\mathbb {R} } a discount factor. Furthermore, a mixed strategy is a measurable function π : E × R + → P ( A ) {\displaystyle \pi :\mathbb {E} \times \mathbb

label Y=r actually was. In theoretical terms, a classifier is a measurable function C : R d → { 1 , 2 , … , K } {\displaystyle C:\mathbb {R} ^{d}\to

1 {\displaystyle \mathbb {P} _{x}[X_{0}=x]=1} . We have for any measurable function f : E → [ 0 , ∞ ] {\displaystyle f\colon E\to [0,\infty ]} the following

. {\displaystyle f={\frac {dX_{*}P}{d\mu }}.} That is, f is any measurable function with the property that: Pr [ X ∈ A ] = ∫ X − 1 A d P = ∫ A f d μ

{\displaystyle (X,\Sigma ,\mu )} and a real-valued essentially bounded measurable function λ {\displaystyle \lambda } on X {\displaystyle X} and a unitary operator

state space R d {\displaystyle \textstyle {\mathbb {R} ^{d}}} and a (measurable) function f {\displaystyle \textstyle f} on R d {\displaystyle \textstyle \mathbb

{\displaystyle Y} , and Z {\displaystyle Z} each be defined as a Borel-measurable function from Ω {\displaystyle \Omega } to some state space endowed with a

_{\Omega }A(x)P(x)\,dx,} where A ( x ) {\displaystyle A(x)} is a (measurable) function of interest. For example, consider a statistic E ( x ) {\displaystyle

{\displaystyle C^{1}} diffeomorphism. If f {\displaystyle f} is a Lebesgue measurable function on G ( Ω ) {\displaystyle G(\Omega )} , then f ∘ G {\displaystyle

multilayer feedforward networks are capable of approximating any Borel measurable function from one finite dimensional space to another to any desired degree

the unit disk D and with limit set the unit circle. Let μ(z) be a measurable function on D with ‖ μ ‖ ∞ < 1 {\displaystyle \|\mu \|_{\infty }<1} such that

compact, f(x,θ) is continuous at each θ ∈ Θ for almost all xs, and measurable function of x at each θ. there exists a dominating function d(x) such that

are a type of order statistic. quota sampling random variable A measurable function on a probability space, often real-valued. The distribution function

L^{*}=\inf _{f}L_{P}(f)} , where f {\displaystyle f} can be any measurable function. Let the function class F {\displaystyle {\mathcal {F}}} be split

quasiconvex function which has the same name. A locally bounded Borel-measurable function f : R m × d → R {\textstyle f:\mathbb {R} ^{m\times d}\rightarrow

0<T\leq \infty } and suppose that φ {\displaystyle \varphi } is a measurable function of the form φ ( t ) = t λ g ( t ) {\displaystyle \varphi (t)=t^{\lambda

f:X\to \mathbb {C} } is a complex-valued Ω {\displaystyle \Omega } -measurable function. There exists a unique largest open subset V f {\displaystyle V_{f}}

easy consequences: If f : X → Y {\displaystyle f:X\to Y} is a Borel measurable function with countable fibers, the image of f {\displaystyle f} is a Borel

the function employed to determine each prisoner's guess is not Measurable function. To see this, consider the case of zero prisoners being killed. This

G({\boldsymbol {w}},.):\mathbb {R} ^{m}\to \mathbb {R} } is a Borel measurable function for all values w ∈ W . {\displaystyle {\boldsymbol {w}}\in {\boldsymbol

uniformly continuous functions: a modulus of continuity Lp for a measurable function f : X → R is a modulus of continuity ω : [0, ∞] → [0, ∞] such that

if the following is true: 9–12  P {\displaystyle P} maps bounded, measurable function on bounded, measurable functions. Let 1 {\displaystyle \mathbf {1}

composition and X − 1 {\displaystyle X^{-1}} is the pre-image of the measurable function or, equivalently, the S T {\displaystyle S^{T}} -valued random variable

to the discrete case, E ( |Z| | g(X) ) = E ( |Z| | X ) for every measurable function g that is one-to-one on (-1,1). Given X = x, the conditional distribution

{z}}}}=\mu (z){\frac {\partial F}{\partial z}},} where μ is the bounded measurable function defined by μ ( z ) = ∂ f ∂ z ¯ / ∂ f ∂ z {\displaystyle \mu (z)={\frac

with domain D {\displaystyle D} , then the surface integral of a measurable function F {\displaystyle F} on M {\displaystyle M} is defined and denoted

{\displaystyle \int _{\gamma }\rho \,|dz|} is the integral of the Borel-measurable function ρ ( γ ( t ) ) {\displaystyle \rho (\gamma (t))} with respect to the

correspondence between mutual-informations functions and finite measurable function of a set with intersection operator, to construct the Čech complex

β s i = t {\displaystyle \beta _{s_{i}}=t} . We then set for any measurable function f {\displaystyle f} : X ^ t N ( f ) := ∑ i = 1 n f ( η s N ( t )

measure zero, the Beltrami coefficient extends uniquely to a bounded measurable function on C. smooth on the regular set. The normalised solution of the Beltrami

paths so that their outputs at any time t {\displaystyle t} is a measurable function of past values of the input and time. For example, stochastic differential

referring to the underlying e-variable (a random variable, that is, a measurable function of the data). A test for a null hypothesis H 0 {\displaystyle H_{0}}

{\displaystyle s\in S} , f ( s ; t ) {\displaystyle f(s;t)} is a bounded and measurable function of t ∈ T {\displaystyle t\in T} . Then F ( s ) = ∫ T f ( s ; t )