Sentence examples for a measurable function from from inspiring English sources

(b) defines a measurable function from into.

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 closedness of F implies ξ is a mapping from Ω to F. Since F is a subset of a separable Banach space X, so, if T is a continuous random operator then by [17, Lemma 8.2.3], the map ω → T ω, f is a measurable function for any measurable function f from Ω to F. Thus {ξ t } is measurable. Hence ξ: Ω → F, being the limit of {ξ t }, is also measurable. Lemma 2.1. [15]).

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).

A rough variable is a measurable function ξ from the rough space ((Lambda,Delta, mathscr{A},pi)) to the set of real numbers.

An uncertain set is a measurable function ξ from an uncertainty space ( Γ, L, M ) to a collection of sets of real numbers, i.e., for any Borel set B of real numbers, the following two sets: { ξ ⊂ B } = { γ ∈ Γ ∣ ξ ⊂ B }, { B ⊂ ξ } = { γ ∈ Γ ∣ B ⊂ ξ }. are events.

The nonadditive set function μ is a mapping from P X) to [0, ∞) where μ=0. Let f: X→ be a measurable function on the measure space (X, F, μ), whose outputs represent the observed target values.

The appropriate restriction is that a random variable must be a measurable function.

where is a measurable function.