Sentence examples for main theorem as from inspiring English sources

We obtain the main theorem as follows.

We state our main theorem as follows.

We have the main theorem as follows.

Then we can prove our main theorem as follows.

Now, we state and prove our main theorem as follows.

More precisely, we state our main theorem as follows.

Based on the above notations, Beardon obtained two main theorems as follows.

Let D k = { x ∈ R n : | x | ≤ 2 k }, A k = D k ∖ D k − 1 for k ∈ Z and χ E be the characteristic function of the set E. Then we can formulate our main theorems as follows.

They introduced a completely new technique based on the concept of X ( x ) to control the growth order of the numerator log M u ( σ, F ) or log μ ( σ, F ), and obtained the main theorems as follows.

Although the compactness of embedding of the working space fails, thanks to the fact that the parameter λ can be taken sufficiently large, two main theorems as regards the existence and multiplicity of nontrivial solutions of (1.6) were obtained via variational methods successfully.

Our main theorem is as follows.