Sentence examples for measurable selection of from inspiring English sources

A measurable function is called a measurable selection of if for every Denote by (2.4).

Then there exists a measurable selection of such that, for any, (21).

Let be two measurable multivalued operators, be a constant and be a measurable selection of.

A measurable mapping is called a measurable selection of the operator if for each.

A operator is called a measurable selection of a multivalued measurable operator if is measurable and for any,.

A measurable selection of F is a measurable map f : Ω → R k satisfying f ∈ F for each ω ∈ Ω.

Since the inf and the sup operators preserve measurability, we see that the functions l F and r F are measurable selections of F. □.

The next lemma shows that l F and r F are measurable selections of F when the latter is measurable.

Then the point functions l F and r F are measurable selections of F. Proof Choose a sequence of measurable selections { f n } n = 1 ∞ of F such that F = ⋃ n ≥ 1 f n ¯.

We present some regularity properties for the set of distributions induced by the measurable selections of a correspondence over a Loeb space, which include closedness, convexity, compactness, purification, and semicontinuity.

Then there exists a sequence ({ f_{n}}) of measurable selections of φ such that, for every x, varphi(x)=overline{bigl{ f_{n}(x mid n inmathbb{N}bigr} }= overline {bigcup_{n inmathbb{N}} f_{n}(x)}, where the bar denotes the closure in X. (cf., e.g., Lemma 7.1 in [36]).