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Non-relativized, Computable and Schnor randomness w.r.t a measure

Does this claim generalize to computable (computable martingales) or Schnor (tests with uniformly computable measures) even in the presence of atoms? … I tagged this with martingales as that is how one defines computable randomness but I'm not sure if the tag should be used (even if technically accurate) to the notion as used in algorithmic randomness …
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