I have started reading the book "The Geometry of moduli of sheaves" by Huybrechts and Lehn. This is a statement in this book at page no.3 the last line.

"E is pure if and only if all associated points of E have the same dimension." Definition for associated points of a sheaf is as follows:

$Ass(E)=\{x∈X|m_x∈AssE_x\}$.

(1). How to prove this statement specially the converse part that if all associated points have the same dimension, then $E$ is pure?

(2). Can anyone suggest me some reference in this regard?