  Let $\mathcal G$ be a family of subsets of an $n$-element set. The family
$\mathcal G$ is called $3$-wise $t$-intersecting if the intersection of any
three subsets in $\mathcal G$ is of size at least $t$. For a real number
$p\in(0,1)$ we define the measure of the family by the sum of
$p^{|G|}(1-p)^{n-|G|}$ over all $G\in\mathcal G$. We prove that if $t\geq 15$
and $p\leq 2/(\sqrt{4t+9}-1)$ then $p^t$ is the maximum measure of $3$-wise
$t$-intersecting families, and the bound for $p$ is sharp. We also present the
corresponding stability result for shifted families.
