Boolean functions with noisy inputs

We consider Boolean functions with noisy inputs. I.e., each binary input is sent over a binary symmetric channel with crossover probability isin before fed into the function. By proving an upper bound for the average l-sensitivity, we show that Boolean functions with average sensitivity less or equal 1 will not amplify the noise at their input. This means, that on average the probability that the output of the function is different from the output of the same function without noise, is less or equal e.