  In this note we give an example of measure satisfying the box condition on
certain sub-bi-trees (see below) but not satisfying Carleson condition on those
sub-bi-trees. This can be considered as a certain counterexample for two weight
bi-parameter embedding of Carleson type. Our type of counterexample is
impossible for a simple tree. In the case of a simple tree, the box condition,
Carleson condition and two weight embedding are all equivalent. In the last
section we show that bi-parameter box condition implies the bi-parameter
capacitary estimate for dyadic rectangles.
