Résumé
A theorem of Kucera states that given a Martin-Lof random infinite binary sequence omega and an effectively open set A of measure less than 1, some tail of omega is not in A. We show that this result can be seen as an effective version of Birkhoff's ergodic theorem (in a special case). We prove several results in the same spirit and generalize them via an effective ergodic theorem for bijective ergodic maps.