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Let $\mathsf{H}^{\rho}_{\text{avg}}(f)$ denote the $\rho$-average case hardness of $f$, which is the largest $S$ such that for every circuit $C$ of size at most $S$, $$ \text{Pr}_{x\in_R\{0,1\}^n}[C(x)=f(x)]<\rho. $$ Statement : Given a distribution $H$ over $\{0,1\}^n$, say has density $\delta$ if for every $x\in\{0,1\}^\ast$, $\text{Pr}[H=x]\leq 1/(\delta 2^n)$.