A Random Sequence of Reals

Since this paper was rejected by a Journal, I will divide the results, extend them and publish by some papers.

News
Jan 11, 2011, Rejected
Aug 2, 2010, Submitted to a Journal

Title
A Random Sequence of Reals

Type
Fullpaper

Journal
Unpublished

Download
preprint
Japanese summary

Abstract
We define a random sequence of reals as a random point on a computable topological space. This randomness has three equivalent simple characterizations, namely, by tests, by martingales and by complexity. We prove that members of a random sequence are relatively random. Conversely a relatively random sequence of reals has a random sequence such that each corresponding member is Turing equivalent. Furthermore strong law of large numbers and the law of the iterated logarithm hold for each random sequence.

Renewal

The following is a history of my site.
Dec 28,2010
The underlying system was changed to WordPress.
Sep 10,2010
The underlying system was changed to Drupal.
Sep 4, 2009
My website was first created by Haru.