Tilde Notation in Additive Combinatorics

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A, B are some finite subsets of a abelian group.

|A + B| ~ |A|

The problem is I couldn't precisely understand what does ~ mean in that case.

For example, it could be found in notes of Tao's lectures on Additive Combinatorics

Page 8, he is defining essentialy B-invariant set.

It is obvious that ~ means that A+B is not much larger than A but I need the precise definition. For me it's a bit too bad using ~ for something else than equivalence relation.

Thanks!