… We prove the effective version of Birkhoff’s ergodic theorem for Martin-Löf random points and
… prove a generalization of Kucera’s theorem, which is a particular case of effective ergodic …

… general version of Birkhoff’s ergodic theorem for random points… for deriving sharper theorems
for random points, sensitive to … (iii) Proving an effective version of Prokhorov theorem, we …

… a constructive proof of Shannon-McMillan-Breiman theorem, … on Birkhoff’s ergodic theorem
for Martin-Löf random sequences. … develop effective versions of Birkhoff’s ergodic theorem. In …

… the points that satisfy Birkhoff’s ergodic theorem under certain … if x is not Martin-Löf random
then x is not weakly Birkhoff for some … is oddly “half-constructive”—we mix the constructive and …

… groups and prove the following versions of effective Birkhoff’s ergodic theorem. Let Γ be
a … For every lower semicomputable f and for every Martin-Löf random \(\omega \in \{ 0,1\}^{\…

… results of ergodic theory like the Birkhoff ergodic theorem – Krengel [12], … constructive version
of the ergodic theorem by V’yugin [21] shows that this sequence ω is not Martin-Löf random…

… surely but for each individual Martin-Löf random sequence. … ergodic theory. First, there are
no universal stability bounds in … results of ergodic theory like Birkhoff’s ergodic theorem – …

… versions of Birkhoff’s theorem. For … point if ϱ(C|z) = 1 for every effectively closed class C
containing z. We say that z is density random if z is a density-one point and Martin–Löf random. …

… prove the constructive version of Birkhoff’s ergodic theorem … Then for every Martin-Löf random
sequence ω there exists … effectively null set in the sense of Martin-Löf: for every rational ε > …

… of the system (Birkhoff’s pointwise ergodic theorem). We prove that a … This notion received
less attention over the years: Martin-Löf’s … So the two bases are constructively equivalent. …