Sentence examples for in addition to the hypothesis of from inspiring English sources

Theorem 2.4 In addition to the hypothesis of Theorem  2.1 (resp.

Theorem 2.5 In addition to the hypothesis of Theorem  2.1, suppose that x 0, y 0 ∈ X are comparable.

If in addition to the hypothesis of Theorem 2.1 (resp., Theorem 2.2) we suppose that, and are comparable, then.

The following result, due to Theorem 2.4 in Luong and Thuan [25] follows by taking A = B. Corollary 2.3 In addition to the hypothesis of Corollary  2.1 (resp.

Corollary 3.7 If, in addition to the hypothesis of Theorem 1.2, we assume that A ∈ F if and only if P ( A ) = 0 of 1, then x ¯ = E ( x ).

Theorem 3.11 In addition to the hypothesis of Theorem  3.4, suppose that for every Y ¯, Y ∗ ∈ X k there exists V ∈ X k such that T ( V ) is comparable to T ( Y ¯ ) and to T ( Y ∗ ).

In addition to the hypotheses of Corollary 3.3.

In addition to the hypotheses of Theorems 3.1 and 3.2, suppose that condition (3.12) holds.

Corollary 15 In addition to the hypotheses of Corollary  4 (resp.

Assume that X is a totally ordered set in addition to the hypotheses of Theorem  3.1.

In addition to the hypotheses of Corollary 4.1, suppose that T is ((alpha,d)) regular.