2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/104726Let phi be a Dubins-Freedman random homeomorphism on [0,1] derived from the base measure uniform on the vertical line x=1/2, and let f be a periodic function satisfying that |f(x)-f(0)| = o(1/log log log 1/x). Then the Fourier expansion of f composed with phi converges at 0 with probability 1. In the condition on f, o cannot be replaced by O. Also we deduce some 0-1 laws for this kind of problems.20 pages. Part of my PhD thesisClassical Analysis and ODEsProbability42A61, 42A20, 60F20, 60B15, 60K99, 39B22text