Sentence examples for proved the implication from inspiring English sources

Billingsley ( 1995 ) proved the implication that (hb) ⇒ (h8) by a version of analytic continuation of characteristic function, but it is easy to see that (hb) also implies (h7) and hence X is M-det on ({mathbb {R}}.) In Theorem 1, Carleman's condition (h7) is the weakest checkable condition for X to be M-det on ({mathbb {R}}).

We prove the implication (i) ⇒ (ii).

It remains to prove the implication:.

Proof We first prove the implication ((i) ⇒ (ii)).

The norm inequality having already been provided by Theorem 4.14, we only have to prove the implication lim r → 0 sup x ∈ R n ∥ f ∥ L Φ ( B ( x, r ) ) φ 1 ( x, r ) = 0 ⟹ lim r → 0 sup x ∈ R n ∥ T b f ∥ L Φ ( B ( x, r ) ) φ 2 ( x, r ) = 0. (4.14).

In any case, further functional studies are required to unequivocally prove the implication of the candidate gene in controlling the proposed volatile accumulation.

Globally, this study has proven the implication of some compounds present in AESb on the rapid maturation of ovarian follicular cells leading to a precocious puberty onset.

Let us prove the implications as follows: (i) (ii) (iii) (iv) (i).