Sentence examples for extend propositions from inspiring English sources

We now extend Propositions 4 7 in [1], which were proved under the i.i.d.i.d

About $7 billion a year in school funding will be at stake this fall when voters decide whether to extend Proposition 30, a tax on high-income Californians. .

But even if activists manage to extend Proposition 30, which fully expires in 2018, and if projections of a long stretch of black ink are correct, it will take years to restore many school districts to pre-recession levels, nevermind to raise base funding from a level that's widely seen as inadequate.

Hence Theorem 2.1 extends Proposition 3.1 in [6].

Lemma 2.5 extends Proposition 4.1 of Chen et al. in [4] and Lemma 2.6 of Zhong-Huang in [6].

Remark 2.8 In special cases as those in Section 1 (d), (e) and (f), (i) Lemma 2.5 extends Proposition 4.1 of Chen et al. in [4] and Lemma 2.6 of Zhong-Huang in [6].

Step 4 extends Proposition 6 by establishing a lower bound on the gap between optimal outputs under the two kinds of contract that holds uniformly for all technologies in G with sufficiently small elasticities of substitution.

From this it follows that ( f n ) n is not ℱ-exhaustive at 0. Moreover, it is not difficult to check that ( f n ) n is ℱ-backward exhaustive at 0, but not ℱ-forward exhaustive at 0. The following two propositions extend [[49], Proposition 3.5] and will be useful in the sequel.

Bounded doubt interpreters must explain why, in the first place, the Evil Genius Doubt's potency does not extend to propositions in the special class.

Granting a bounded doubt interpretation, why — in the first place — does the Evil Genius Doubt's potency not extend to propositions in the special class?

The aim of this section is to extend the Proposition 1 in [6] and Theorem 2.2 to functions of several variables defined on invex subsets of.