FKN Theorem on the biased cube

In this note we consider Boolean functions dened on the discrete cubef ; 1 g n equipped with a product probability measure n , where = + 1 and = p = . We prove that if the spectrum of such a function is concentrated on the rst two Fourier levels, then the function is close to a certain function of one variable. Moreover, in the symmetric case = = 1 we prove that if

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