Résumé
Fields of Logic and Computation, Lecture Notes in Computer
Science, v.9300 (2015) A remarkable achievement in algorithmic randomness and algorithmic
information theory was the discovery of the notions of K-trivial, K-low and
Martin-Lof-random-low sets: three different definitions turns out to be
equivalent for very non-trivial reasons. This paper, based on the course taught
by one of the authors (L.B.) in Poncelet laboratory (CNRS, Moscow) in 2014,
provides an exposition of the proof of this equivalence and some related
results. We assume that the reader is familiar with basic notions of
algorithmic information theory.