Footnotes
... modified1
As pointed out by M. Hutter (14 Nov. 2000, personal communication) and even earlier by A. Fujiwara (1998, according to P. M. B. Vitányi, personal communication, 21 Nov. 2000), the proof on the bottom of p. 249 of [#!LiVitanyi:97!#] should be slightly modified. For instance, the sum could be taken over $x_{i-1}<x\leq x_i$. The sequence of inequalities $\sum_{x_{i-1}<x\leq x_i}P(x)>x_iP(x_i)$ is then satisfiable by a suitable xi sequence, since $\liminf_{x\to\infty}\{xP(x)\}=0$. The basic idea of the proof is correct, of course, and very useful.
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Juergen Schmidhuber
2001-01-09


Related links: In the beginning was the code! - Zuse's thesis - Life, the universe, and everything - Generalized Algorithmic Information - Speed Prior - The New AI