Sentence examples for be any compact interval from inspiring English sources

Let be any compact interval and as in Theorem 3.9.

Let ([a,b]) be any compact interval of (mathbb{R}).

(I) Let (Isubset J) be any compact interval.

Let be any compact interval,,, where, are nonnegative real weights such that and.

Let (n=1) and let ([a,b]) be any compact interval.

The set of the functions for which the above convergence is uniform on any compact interval is denoted by.

M is uniformly bounded in ℬ; The functions belonging to M are equicontinuous on any compact interval of [ 0, ∞ ) ; The functions from M are equiconvergent, that is, given ϵ > 0, there corresponds a T > 0 such that | f ( t ) − f | < ϵ for any t ≥ T and f ∈ M. Definition 2.1 An operator is called completely continuous if it is continuous and maps bounded sets into relatively compact sets.

Then Ω is relatively compact in E if the following conditions hold: (a) Ω is uniformly bounded in E;   (b) the functions belonging to M are

Let ℬ be defined as before and M ⊂ B. Then M is relatively compact in ℬ if the following conditions hold: (a) M is uniformly bounded in ℬ;   (b) The functions belonging to M are equicontinuous on any compact interval of [ 0, ∞ ) ;   (c) The functions from M are equiconvergent, that is, given ϵ > 0, there corresponds a T > 0 such that | f ( t ) − f | < ϵ for any t ≥ T and f ∈ M.  .

If (V_{1}) is equicontinuous on any compact interval of (mathbb{R}^) and equiconvergent at infinity, then V is relatively compact on E. Assume (H1) holds, then (T Prightarrow P) is completely continuous.

If is C-regular and is absolutely continuous on any compact interval of, then and are differential for a.e., and one has (28).