Sentence examples for application of the dominated from inspiring English sources

Proposition 4.1.2 We have G μ ⟶ μ → ∞ G ∞. Proof It is a direct application of the dominated convergence theorem using the fact that: S ( μ y ) ⟶ μ → ∞ H ( y ) a.e.

Then, a direct application of the dominated convergence theorem and continuity theorems of integrals with respect to parameters show that the function I ( N ) is continuous on N on [ 0, ∞ ).

The proof in the case \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H(F^{(1)})\mathrm{(iiib)}$$\end{document} H (F (1 ) ) (iiib ) follows by a direct application of the Lebesgue dominated convergence theorem.

Therefore, before application any surfactants, hydrocarbon uptake mechanisms of the dominate degrader should be defined.

A direct application of dominated convergence theorem shows that the right hand side converges to 0 as N → ∞ since s N exp ( − s b N a 0 ) is a bounded function uniform in N and s.

The analysis shows that reports about the applications of nanotechnology dominate the media coverage.

We now deduce that T x m → T x in C 1 ( I ) thanks to standard properties of the Green's function and a straightforward application of Lebesgue's dominated convergence theorem.

Moreover, the function I ( N ) is C ∞ on N since all their derivatives can be computed by differentiating under the integral sign by direct application of dominated convergence theorems and differentiation theorems of integrals with respect to parameters.

Hence, we remove one dominated element in each application of the last rule, and terminate when the second rule is applied.

Over the 19th century, the application of the least action principle dominated the approach of analytical dynamics to physical problems.

The latest applications of CARs are dominated by in vivo cascades and chemo-enzymatic reaction sequences.