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Martin-Löf randomness and other randomness notions arising from computable tests; as well as related concepts such as Kolmogorov complexity, K-triviality, and effective Hausdorff dimension.
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What is the precise relation between Kolmogorov complexity and Shannon's entropy?
What follows, which is all standard stuff (and should be in, say, Li and Vitanyi's monograph, or Downey and Hirschfeldt perhaps), might be the sort of relationship you vaguely recall seeing.
Your $R( …