  Leonid Levin (arxiv.org/abs/cs/0503039v14, p.7) published a new (and very
nice) proof of G\'acs-Ku\v{c}era'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. Then we
review the previous work about the oracle use when reducing a given sequence to
another one, and its connection with algorithmic dimension theory.
