2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/219499We study the range of validity of differentiation theorems and ergodic theorems for $\R^d$ actions, for averages on "thick spheres" of Euclidean space.Dynamical SystemsClassical Analysis and ODEsAverages on annuli of Eulidean spacetext