We show that any sequence of well-behaved (e.g. bounded and non-constant) real-valued functions of $n$ boolean variables $\{f_n\}$ admits a sequence of coordinates whose $L^1$ influence under the $p$-biased distribution, for any $p\in(0,1)$, is $\Omega(\text{var}(f_n) \frac{\ln n}{n})$.
翻译:我们证明,对于任意表现良好(如有界且非常值)的n元布尔变量实值函数序列$\{f_n\}$,在任意$p\in(0,1)$的偏置分布下,总存在坐标序列使得其$L^1$影响达到$\Omega(\text{var}(f_n) \frac{\ln n}{n})$量级。