Sentence examples for for given measurable from inspiring English sources

Then, for given measurable, we have (3.6).

Then, for given measurable, one has (27).

If,,,, and are the same as in Algorithm 2.4, then, for given measurable, we have (28).

Corollary 3.2 Let X, K, T be as in Theorem 3.1, for any given measurable mapping ξ: Ω → K, then (i) for each t ∈ (0, 1), there exists a unique measurable mapping ξ t from Ω into X such that ξ t = t ξ + ( 1 - t ) T ( ω, ξ t for each ω ∈ Ω.   (ii) T has a random fixed point if and only if {ξ t } is bounded as t → 0 for each ω ∈ Ω.

For any given measurable mapping, the multivalued mappings are measurable by Lemma 2.5.

For a given measurable function (varphi Irightarrowmathbb{R}^{d}), the composite operator (mathcal{N}_{psi}varphi(cdot):=psi(cdot,varphi(cdot))) which maps I into (mathbb{R}) is said to be a nonautonomous type superposition operator.

Then, for a given measurable space ( Ω, F ) consisting of a k-dimensional Euclidean space Ω and its Borel subset, the mappings of quantizer q can be described as follows: Encoder ϕ: Ω → I, where is a countable index set.

For a given measurable function ψ : I → R, the composite operator N f ∘ ψ : = f which maps I into ℝ is said to be a nonautonomous type superposition operator.

Tree ring and carbon isotope analysis of a sample of trees on the study sites would give measurable data for evaluating this question, which would be a good field study to follow this modeling exercise.

Neither dibromochloromethane nor bromoform gave measurable breath concentrations for any of the activities investigated because of their much lower tap-water concentrations.

As a result of the much lower DBCM and bromoform concentrations in the tap water in this study, neither chemical gave measurable breath concentrations for any of the water-use activities investigated (Nuckols et al. 2005).