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We show that certain statements related to the Fourier-Walsh expansion offunctions with respect to a biased measure on the discrete cube can be deducedfrom the respective results for the uniform measure by a simple reduction. Inparticular, we present simple generalizations to the biased measure $\mu_p$ ofthe Bonami-Beckner hypercontractive inequality, and of Talagrand's lower boundon the size of the boundary of subsets of the discrete cube. Ourgeneralizations are tight up to constant factors.

A simple reduction from a biased measure on the discrete cube to the uniform measure