Sentence examples for main theorem characterizes from inspiring English sources

For convex domains, our main theorem characterizes truthful social choice functions as those satisfying two properties: local weak monotonicity and vortex-freeness.

In a previous paper we showed how the main theorems characterizing operator algebras and operator modules, fit neatly into the framework of the "noncommutative Shilov boundary," and more particularly via the left multiplier operator algebra of an operator space.

Based on some basic results from the theory of orthogonal polynomials, as summarized in Section 2, we characterize in the main Theorem 3.1 these sets of finite atomic random variables.

Theorem 3.3 (main theorem).

The main theorem follows.

Example of main theorem.

The following theorem is our main theorem.

This proves our main theorem.

The proof of Main Theorem.

The following theorem characterizes that case.

We can now state the main theorem.