Abstract: Rearrangement Lemma is a very deep result that first was stated and proved by Connes. He proved it to integrate a vector valued function while studying the geometry of noncommutative 2-tori with a conformally perturbed metric. In our recent work joint with Masoud Khalkhali and Ali Moatadelro, on the noncommutative 3-torus, we have proved a slightly different version of that. In this talk I will give a proof of that version of Rearrangement Lemma.