Probability Measures and Effective Randomness

Mathematics – Logic

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

9 pages

Scientific paper

We study the question, ``For which reals $x$ does there exist a measure $\mu$ such that $x$ is random relative to $\mu$?'' We show that for every nonrecursive $x$, there is a measure which makes $x$ random without concentrating on $x$. We give several conditions on $x$ equivalent to there being continuous measure which makes $x$ random. We show that for all but countably many reals $x$ these conditions apply, so there is a continuous measure which makes $x$ random. There is a meta-mathematical aspect of this investigation. As one requires higher arithmetic levels in the degree of randomness, one must make use of more iterates of the power set of the continuum to show that for all but countably many $x$'s there is a continuous $\mu$ which makes $x$ random to that degree.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Probability Measures and Effective Randomness does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Probability Measures and Effective Randomness, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Probability Measures and Effective Randomness will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-453491

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.