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I am reading this paper $ <$Interlacing Families IV: Bipartite Ramanujan Graphs of All Sizes$>$, which proved the existence of the Ramanujan Graphs of all sizes.

This paper uses the notion of Haar measure on $O(n)$, the orthogonal group on $\mathbb{R}^n$. I searched on Google and Wiki about this but it is too hard for me since I am not familiar with abstract measure theory.

I am wondering if there is an easier way to understand the specific example, which is the Haar measure on $O(n)$. What I know about measure theory is the Lebesgue meausre and to construct the integral given an meausre.

Nate
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