The previous section covered the case of $f \in L^2(\Omega^n, \pi^{\otimes n})$ with $|\Omega| = 2$; there, we saw it could be helpful to look at explicit Fourier bases. When $|\Omega| \geq 3$ this is often not helpful, especially if the only “operation” on the domain is equality. For example, if $f : \{\mathsf{Red}, [...]

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Ohad Klein: Are the indexing in (the start of) 7 OK?Ohad Klein: "learning algorithm running in time in time"Amir: In the proof of Theorem 16, and in the equation immediately ...Ohad Klein: In example 6, should "of codimension less than n" be "of pos...Ohad Klein: In 15c (18c in the book), I think it should be $\cap_j{V_j}$...Ohad Klein: Bracket typo: In the proof of thm 10 (12 in the book), $sgn(...Ohad Klein: Oops, my bad.