A note on the Entropy/Influence conjecture

The Entropy/Influence conjecture, raised by Friedgut and Kalai (1996) [9], seeks to relate two different measures of concentration of the Fourier coefficients of a Boolean function. Roughly saying, it claims that if the Fourier spectrum is “smeared out”, then the Fourier coefficients are concentrated on “high” levels. In this note we generalize the conjecture to biased product measures on the discrete cube.