  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 $G\in{\mathcal G}$. For example, if ${\mathcal
G}$ consists of all subsets containing a fixed $t$-element set, then it is a
$3$-wise $t$-intersecting family with the measure $p^t$.
  Let $0<p\leq 2/(\sqrt{4t+9}-1)$, $\delta>0$, and let ${\mathcal G}$ be a
$3$-wise $t$-intersecting family. It is known that the measure of ${\mathcal
G}$ is at most $p^t$. Suppose, moreover, that ${\mathcal G}$ has the measure at
least $(\frac12+\delta)p^t$. We show that, by choosing $t$ sufficiently large
depending on $\delta$, the structure of ${\mathcal G}$ is one of (i) and (ii):
(i) every subset in ${\mathcal G}$ contains a fixed $t$-element set, (ii) every
subset in ${\mathcal G}$ contains at least $t+2$ elements from a fixed
$(t+3)$-element set.
