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Analysis of Boolean Functions by Ryan O'Donnell

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Chapter 8 Generalized Domains

So far we have studied functions f : {0, 1}n. What about, say, f : {0, 1, 2}n? In fact, very little of what we’ve done so far depends on the domain being {0, 1}n; what it has mostly depended on is our viewing the domain as a product probability distribution. Indeed, much of analysis of Boolean functions carries over to the case of functions f : Ω1 × · · · × Ωn where the domain has a product probability distribution ...

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