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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:

$Ass(E) = \{x \in X \vert m_x \in AssE_x \}$.

Point has always dimension 0 ,So my question is, what does this mean by saying that associated points have same dimension?

Does this mean that local rings $O_x$ has the same dimension for all $x$ associated point of $E$ ?

Can anyone suggest me a good reference which supports me while studying this book?

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    In scheme-theoretic algebraic geometry, the dimension of a point is not always $0$... – 2017-01-16
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    @Tabes Bridges Where can i find an example of this? – 2017-01-17
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    With the dimension of a point, they mean the dimension of its closure. For instance for an integral scheme the dimension of the generic point is equal to the dimension of the scheme. – 2017-01-17
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    @MooS can you provide me proof of this? – 2017-01-17
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    A proof of what? I just clarified the definition. – 2017-01-17
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    @MooS I want proof of "E is pure if and only if all associated points of E have the same dimension." – 2017-01-17

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I found a P.hd. thesis by Alain Leytem entitled with "Torsion and purity on non-integral schemes and singular sheaves in the fine Simpson moduli spaces of one-dimensional sheaves on the projective plane ".The above asked question is answered there and give a good exposition to the relation between torsion sheave and purity of coherent sheaves over Noetherian scheme. Link is given below: http://orbilu.uni.lu/handle/10993/23380