Then, T is said to be a ψ-multivalued weakly Picard operator (briefly ψ-MWP operator) if and only if ψ : ℝ+→ ℝ+ is a continuous in t = 0 and increasing function such that ψ(0) = 0, and there exists a selection t∞ of T∞ such that d ( x, t ∞ ( x, y ) ) ≤ ψ ( d ( x, y ) ), f o r a l l ( x, y ) ∈ G r a p h ( T ).
There may also exist a selection bias in favor of young and highly productive researchers who would not have been hired if they had had a lower level of productivity.
A separate laboratory-based sentinel system exists for a selection of viral pathogens [ 4].
Then there exists a measurable selection of such that, for any, (21).
Then Since is open, is open in From Theorems 2.1 and 2.2, there exists a continuous selection of and such that for every, (3.10).
Then, (1) is measurable if and only if Graph is measurable; (2)if is measurable and is closed a.e., then there exists a measurable selection of.
If only lists of facilities in a country existed a random selection of these lists was made.
[12]Let M, V : Ω → CB X) be two measurable set-valued mappings, ϵ > 0 be a constant and x : Ω → X be a measurable selection of M. Then there exists a measurable selection y : Ω → X of V such that, for any t ∈ Ω, x ( t ) - y ( t ) ≤ ( 1 + ∈ ) Ĥ ( M ( t ), V ( t ) ).
Let (T_{1}, T_{2}:Omegato operatorname{CB}(H)) be two measurable multi-valued mappings, (epsilon> 0) be a constant, and (w_{1}:Omegato H) be a measurable selection of (T_{1}), then there exists a measurable selection (w_{2}:Omegato H) of (T_{2}) such that for all (tinOmega), biglVert w_{1}(t -w_{2}(t -w_{2}rt bigrVertpsileq){hat{H}}bigl(T_{1+(t),T_{2}(t)bigr).
By virtue of the Aumann-type selection theorem (see Lemma 7.2), there exists a measurable selection (vcolonOmegato X) of F which completes the proof.
