Sentence examples for is continuous in there from inspiring English sources

Since is continuous in, there exists a constant, such that, for.

Since is continuous in, there exists such that for all (323).

On the other hand, for, since is continuous in, there exists small enough such that.

If for each the mapping is continuous in, then there exists a unique -quadratic mapping such that (2.37).

satisfying for all If for each the mapping is continuous in, then there exists a unique -quadratic mapping satisfying (2.45).

Let be a constant such that for all If for each the mapping is continuous in, then there exists a unique -quadratic mapping satisfying (2.20).

By a similar method to the proof of Theorem 2.3, one can show that if for each the mapping is continuous in, then there exists a unique -quadratic mapping satisfying (2.40).

satisfying for all By a similar method to the proof of Theorem 2.7, one can show that if for each the mapping is continuous in, then there exists a unique -quadratic mapping satisfying (2.58).

By a version of the analytic Fredholm theorem (see [494, Theorem VI.14]), there is a set ({mathcal {E}}subset (0,infty )), so that ({mathcal {E}}) is a closed set (i.e. its only limit points are in ({mathcal {E}}) or are 0 or (infty )) of (real) Lebesgue measure 0 and so that if (z notin {mathcal {E}}), then (({varvec{1}}-B z))^{varvec{1}}-B zd is continuous in z there.

Because |f0 x)| is continuous in [0, a], there exists the maximum value, M of |f0 x)| in [0, a].

Proof Because x ≥ 0 and it is continuously differentiable in [0, a], |f0 x)| is continuous in [0, a] and there is the maximum value of |f0 x)| in the range of [0, a].