Gács-Kučera's Theorem Revisited by Levin

10/31/2021

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by   Alexander Shen, et al.

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Leonid Levin (arxiv.org/abs/cs/0503039v14, p.7) published a new (and very nice) proof of Gács-Kučera's theorem that occupies only a few lines when presented in his style. We try to explain more details and discuss the connection of this proof with image randomness theorems, making explicit some result (see Proposition 4) that is implicit in Levin's exposition.