We study the a priori semimeasure of sets of Pθ-random infinite sequences, where Pθ is a family of probability distributions depending on a real parameter θ. In the case when for a computable probability distribution Pθ an effectively strictly consistent estimator exists, we show that Levin's a priory semimeasure of the set of all Pθ-random sequences is positive if and only if the parameter θ is a computable real number. We show that the a priory semimeasure of the set∪θ, where Iθ is the set of all Pθ-random sequences and the union is taken over all algorithmically non-random θ, is positive.
- A priory semimeasure
- Algorithmic information theory
- Bernoully sequences
- Martin-Löf random sequences
- Parametric families of probability distributions
- Probabilistic machines
- Turing degrees