= Biased measure of a set family
{title2=$\mu_p(\mathcal F)=\sum_{A\in\mathcal F}p^{|A|}(1-p)^{n-|A|}$}
The <biased measure of a set family> is its probability when each ground-set element is independently included with probability $p$. If $a_j$ is the proportion of the $j$th level occupied by the family, then $\mu_p(\mathcal F)=\sum_j\binom nj a_jp^j(1-p)^{n-j}$. This translates a combinatorial level bound into a probability inequality for independent <Bernoulli random variables>.
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