A constructive version of Birkhoff's ergodic theorem for Martin-Löf random points. Bienvenu, L., Day, A. R., Hoyrup, M., Mezhirov, I., & Shen, A. Information and Computation, 210:21–30, 2012.
A constructive version of Birkhoff's ergodic theorem for Martin-Löf random points [link]Paper  doi  bibtex   
@ARTICLE{BDH+12,
  author = {Bienvenu, Laurent and Day, Adam R. and Hoyrup, Mathieu and Mezhirov,
	Ilya and Shen, Alexander},
  title = {A constructive version of {B}irkhoff's ergodic theorem for {M}artin-{L}\"of
	random points},
  journal = {Information and Computation},
  year = {2012},
  volume = {210},
  pages = {21--30},
  doi = {10.1016/j.ic.2011.10.006},
  file = {BDH+12.pdf:BDH+12.pdf:PDF},
  issn = {0890-5401},
  keywords = {bib,cca},
  mrclass = {03D32 (28D05 37A30 68Q30)},
  mrnumber = {2878799 (2012m:03108)},
  mrreviewer = {Liang Yu},
  owner = {Vasco},
  timestamp = {2013.11.14},
  url = {http://dx.doi.org/10.1016/j.ic.2011.10.006}
}

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