Tree ensembles are looked at in distribution space, that is, the limit case of "infinite" sample size. It is shown that the simplest kind of trees is complete in D-dimensional $L_2(P)$ space if the number of terminal nodes T is greater than D. For such trees we show that the AdaBoost algorithm gives an ensemble converging to the Bayes risk.
"Population theory for boosting ensembles." Ann. Statist. 32 (1) 1 - 11, February 2004. https://doi.org/10.1214/aos/1079120126