2 problems

Let $f:(\{0,1\}^n,\mu_p^n)\to\{\pm1\}$ be Boolean-valued and let $0<p<1$. Define … and let $h(q)=-q\log q-(1-q)\log(1-q)$ be the binary entropy function. Binary-entropy lower-bound…

Let $0<p<1$, let $n$ be positive, and let $f:(\{0,1\}^n,\mu_p^n)\to\{\pm1\}$ be Boolean-valued. Write … and ${\rm I}^{(p)}[f]=\sum_{i=1}^n{\rm Inf}_i^{(p)}[f]$. Keller–Mossel–Schla…