Sentence examples for measurable selector of from inspiring English sources

A measurable (single-valued) operator ξ : Ω → X is called a measurable selector of a measurable operator T : Ω → X if ξ ∈ T for each ω ∈ Ω.

Let (g_{n} x,u,nabla u)) be locally Lipschitz with respect to u, measurable selector of (H_{n} x,u,nabla u)) postulated from Lemma 2.4.

Let (w_{n} t, u)) be measurable selector of (mathcal{F}_{n} t,u)) generated by Lemma 2.1, the locally Lipschitz continuous in (uin H).

It follows from Lemma 2 that for each ω ∈ Ω, P has at least one fixed point in W. Since ⋂ ω ∈ Ω int W ≠ ∅, the hypothesis that a measurable selector of intW exists holds.

Kuratowski and Ryll-Nardzewski's theorem about the existence of measurable selectors for multi-functions is one of the keystones for the study of set-valued integration; one of the drawbacks of this result is that separability is always required for the range space.

Results about norm-Borel measurable selectors for multi-functions satisfying stronger measurability properties but without the classical requirement of the range Banach space being separable are also obtained.

Then F has a measurable selector.

Hence, for any, admits a measurable selector.

Then by virtue of hypothesis (H(F _{2})(i), for every (ngeq1), (xrightarrow H x,s_{n},r_{n},t_{n})) admits a measurable selector (g_{n}(x)).

Then by virtue of hypothesis H ( F ) 2 (i), for every n ≥ 1, t → F ( t, s n ) admits a measurable selector f n ( t ).

A weakly measurable correspondence with non-empty closed values from a measurable space into a Polish space admits a measurable selector.