Abstract:We prove a Central Limit Theorem (CLT) for Martin-Löf Random (MLR) sequences. Martin-Löf randomness attempts to capture what it means for a sequence of bits to be "truly random". By contrast, CLTs do not make assertions about the behavior of a single random sequence, but only on the distributional behavior of a sequence of random variables. Semantically, we usually interpret CLTs as assertions about the collective behavior of infinitely many sequences. Yet, our intuition is that if a sequence of bits is "truly… Show more
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