  The theory of Carleson measures, stopping time arguments, and atomic
decompositions has been well-established in harmonic analysis. More recent is
the theory of phase space analysis from the point of view of wave packets on
tiles, tree selection algorithms, and tree size estimates. The purpose of this
paper is to demonstrate that the two theories are in fact closely related, by
taking existing results and reproving them in a unified setting. In particular
we give a dyadic version of extrapolation for Carleson measures, with two
separate proofs, as well as a two-sided local dyadic $T(b)$ theorem which
generalizes earlier $T(b)$ theorems of David, Journe, Semmes, and Christ.
