A comparison Theorem for matrix limitation methods with applications

A comparison Theorem for matrix limitation methods is proved and the following applications are given: - new results concerning the comparison between weighted densities generated by different weights; - new results concerning the comparison between weighted densities of a set $E \subseteq N^*$ and those of its transformed set $\pi(E)$, where $\pi$ is a given injective function $N^*\to^* ! N¤$. In particular, a new class of permutations preserving the asymptotic density is identified.