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In this paper we study functions with low influences on product probability spaces. These are functions f W 1 n ! that have EOEVar i OEf small compared to VarOEf for each i . The analysis of boolean functions f W f 1; 1g n ! f 1; 1g with low influences has become a central problem in discrete Fourier analysis. It is motivated by fundamental questions arising from the construction of probabilistically checkable proofs in theoretical computer science and from problems in the theory of social choice in economics.
Mossel et al. (Wed,) studied this question.