The gorgeous book "Discrete groups, expanding graphs and invariant measures" by A. Lubotzky investigates the structures that give rise to measure-theoretic phenomena like the B-T paradox. It is a graduate level monograph, but I recommend it wholeheartedly. It illustrates how the study of some paradoxes from the early 20th Century led to amazing and highly applicable mathematics like expander graphs and the spectral theory of non-commutative groups.
