Using almost-everywhere theorems from analysis to study randomness. Miyabe, K., Nies, A., & Zhang, J. The Bulletin of Symbolic Logic, 22(3):305–331, 2016.
Using almost-everywhere theorems from analysis to study randomness [link]Paper  doi  bibtex   
@ARTICLE{MNZ16,
  author = {Miyabe, Kenshi and Nies, Andr\'e and Zhang, Jing},
  title = {Using almost-everywhere theorems from analysis to study randomness},
  journal = {The Bulletin of Symbolic Logic},
  year = {2016},
  volume = {22},
  pages = {305--331},
  number = {3},
  doi = {10.1017/bsl.2016.10},
  file = {MNZ16.pdf:MNZ16.pdf:PDF},
  issn = {1079-8986},
  keywords = {bib, cca},
  mrclass = {03D32 (37A25 60F15 60G46)},
  mrnumber = {3569255},
  mrreviewer = {Johanna N. Y. Franklin},
  url = {http://dx.doi.org/10.1017/bsl.2016.10}
}

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