Sentence examples for the convergence implies from inspiring English sources

(d) A set is called ρ-closed if for any sequence of, the convergence implies that f belongs to B.   (e) A set is called ρ-bounded if.  .

A set is called ρ-closed if for any sequence of, the convergence implies that f belongs to B. A set is called ρ-bounded if.

We show that, in most cases, the convergence implied in such decompositions holds not only in the distributions sense, but also in the function spaces themselves.

We therefore deduce that the ordinary convergence implies the -convergence to the same limit.

Note that the complete convergence implies the almost sure convergence in view of the Borel Cantelli lemma.

The L1 convergence implies the a.e.

Without loss of generality, we assume L > 1 and ε < 1.Set β = ε h p.Since the modular convergence implies the norm convergence, so we can find δ > 0 suchthat I Φ ( y ) ≤ δ implies ∥ y ∥ Φ, p ≤ min { β 2, ε 1 p β 1 − 1 p 2 }.

Hence the uniform convergence implies that v is also continuous.

Since the ordinary convergence implies ideal convergence, I is a regular sequential method [54].

From (1.5), we obtain that the complete moment convergence implies the complete convergence, that is, under the conditions of Theorem A, result (1.4) implies that (1.6).

It is well known that the complete moment convergence implies the complete convergence.