Sentence examples for measurable ii from inspiring English sources

Suppose that there exists a null-measure set such that the following conditions hold: (i for every, is measurable; (ii)for every and all one has either (2.1) or (2.13).

Assume that: (i) the multifunction F is ({mathcal{T}}_{mu}otimes{mathcal{B}}(W -weakly measurable;   (ii) for a.e.

A function is said to be an -Carathéodory function if it satisfies the following: (i for each, is measurable; (ii)for a.e., is continuous; (iii)for any, there exists such that.

(H1) The function verifies the following conditions: (i) the function is continuous for every, and for every, the function is strongly measurable,   (ii) there exist and a continuous nondecreasing function, such that, for all.

The function verifies the following conditions: (i) the function is continuous for every, and for every, the function is strongly measurable,   (ii) there exist and a continuous nondecreasing function, such that, for all.  . the function is continuous for every, and for every, the function is strongly measurable, there exist and a continuous nondecreasing function, such that, for all.

The family { Λ ω ∈ B ( X, H ω ) : ω ∈ Ω } is a Bochner pg-frame for X with respect to { H ω } ω ∈ Ω if: (i) For each x ∈ X, ω ↦ Λ ω ( x ) is Bochner measurable,   (ii) there exist positive constants A and B such that A ∥ x ∥ ≤ ( ∫ Ω ∥ Λ ω ( x ) ∥ p d μ 1 p ≤ B ∥ x ∥, x ∈ X. (2.1)  .

The process (X t)) is called a strong solution of (1.1) if the following three conditions are satisfied: (i) (X t)) is (mathcal{F}_{t} -measurable;   (ii) the integrals in (1.1) exist;   (iii) (mathbb{P}(Xi) = 1) where Ξ is the set oF}_{t} -measurableuch that (1.1) holds for all (t ii [0, the.  .

(i) and are bounded measurable functions; (ii),, where.

Then, and satisfy one of the following items: (i) and are bounded measurable functions,   (ii),,.

Also if generalized function satisfies (1.6), then satisfies one of the followings: (i) and are bounded measurable functions, (ii),,.

Then, and satisfy one of the following items: (i) and are bounded measurable functions,   (ii) and is a bounded measurable function,   (iii),,   (iv),   (v),,   (vi),,  . and are bounded measurable functions, and is a bounded measurable function,,,,,,,, where,,, and is a bounded measurable function.