Sentence examples for our assumption implies that from inspiring English sources

As (u,zin F f)), our assumption implies that z and u are comparable.

Proof First of all, our assumption implies that there exists β > 0 such that r k β ≤ f ( k, β ) for all  k ∈ [ 2, N − 1 ] Z.

Our assumption implies that at small tumour size, the fraction of the resources appropriated by the tumour is approximately proportional to tumour size.

Since our assumption imply that (L*) N A j (x) = O (λ -N ), the result follows.

Such an assumption implies that hasn't happened in the past and won't happen again in the future.

Our assumptions imply that the group does not have a formal mechanism of (or an institution for) achieving a joint decision (such as democratic voting with votes being counted and/or somehow averaged).

Our assumptions imply that news about one style can a ffect the prices of other apparently unrelated styles, that assets in the same style will comove too much while assets in di fferent styles comove too little, and that high average returns on a style will be associated with common factors for reasons unrelated to risk.

Our assumptions imply that (L cap G(x_{i})) is ρ-closed for every (i=1,2,ldots,n).

Claim 3 and our assumptions imply that one of the following holds.

Proof Our assumptions imply that ( I, T ) is an -generalized contraction pair.

Our assumptions imply that L ∩ G(f i ) is ρ-closed for every i = 1, 2,..., n.