## From index sets to randomness in $$\emptyset ^{n}$$: Random reals and possibly infinite computations. II.(English)Zbl 1163.03023

[For Part I see J. Symb. Log. 70, No. 3, 891–913 (2005; Zbl 1089.03037).]
The paper constructs a significant class of examples of $$n$$-random reals which are probabilities that a universal monotone Turing machine performing possibly infinite computations on infinite inputs produces an output in a given set.

### MSC:

 03D80 Applications of computability and recursion theory 03D10 Turing machines and related notions 68Q30 Algorithmic information theory (Kolmogorov complexity, etc.)

Zbl 1089.03037
Full Text:

### References:

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