Sentence examples for measurable function from from inspiring English sources

(b) defines a measurable function from into.

MLP is capable of approximating any measurable function from one finite-dimensional space to another within a desired degree of accuracy (HornikK and White 1989).

f is a Carathéodory function if and only if (omegato r omega)(cdot)=f omega,cdot)) is a measurable function from Ω to (C X,Y)).

A fuzzy rough variable, very different from the fuzzy rough set introduced by Dubois and Prade [6], was defined by Liu [5] as a measurable function from a rough space to the set of fuzzy variables.

Liu [5] defined a rough variable to be a measurable function from a rough space to the set of real numbers and gave the definition of the lower and upper approximations of the rough variable.

Then ( z, D u ) is a Radon measure in Ω, ∫ Ω ( z, D w ) = ∫ Ω z ⋅ ∇ w d x for all w ∈ W 1, 1 ∩ L ∞ , and ( z, D w ) is absolutely continuous with respect to ∥ D w ∥ with the Radon-Nikodým derivative θ ( z, D w, x ) which is a ∥ D w ∥ measurable function from Ω to ℝ such that ∫ B ( z, D w ) = ∫ B θ ( z, D w, x ) ∥ D w ∥ for any Borel set B ⊆ Ω.

Let be all Lebesgue measurable functions from to.

Let A be the set of bounded measurable functions from S to ℝ.

will denote the space of finitely valued and finitely supported measurable functions from into, that is, (1.11).

L p ( J, R ) ( 1 ≤ p < ∞ ) is the Banach space of all Lebesgue measurable functions from J into ℝ with ∥ m ∥ L p ( J, R ) < ∞.

Let (L^{infty}([0,1],R^{N})) be a space of measurable functions from ([0,1]) into (R^{N}) and essentially bounded with the following norm: begin{aligned} |q|_{L^{infty}([0,1],R^{N})}:= operatorname{esssup}bigl{ bigl|q(t bigr|:tin[0,1]bigr}.