Given a mixing action
L
L
of a group
G
G
and a set
A
A
of half measure we consider the possible limits of the measures
μ
(
A
∩
L
m
i
A
∩
L
n
i
A
)
\mu (A\cap L^{m_{i}}A\cap L^{n_{i}}A)
as
i
→
∞
i\to \infty
and
m
i
,
n
i
,
m
i
−
n
i
→
∞
m_{i},n_{i},m_{i}-n_{i}\to \infty
. If the action is 3-mixing, then these limits are always equal to
1
/
8
1/8
. In the Ledrappier example, this limit is zero for some sequences. The following question is studied: what can be said about actions if one of these limits is positive but small? In the paper we make several observations on this topic.
Bibliography: 11 titles.