Sentence examples for need the hypothesis from inspiring English sources

Remark 2.1 In our presented theorems we don't need the hypothesis: ψ is lower semicontinuous.

Remark 3.9 In Theorem 3.6, we do not need the hypothesis of approximate compactness to B. Therefore, Theorem 3.6 improved substantially the results of Theorem 3.4.

We need the hypotheses as follows: (H1) satisfies is measurable for all and is continuous for a.e., and there exist a positive function and a continuous nondecreasing function, such that (3.1).

We need the following hypothesis: for any and there exists a such that (B).

In order to prove our main results, we need the following hypothesis.

We need the following hypotheses.

We need the following hypotheses on the data of (3.1).

To establish the result, we need the following hypotheses.

To do this, we need the following hypotheses.

We need the following hypotheses: (B1) The system of the generalized eigenspaces of A is complete.

We will need the following hypotheses on the data problem (3.1).