Theory of Computing Systems

, Volume 52, Issue 1, pp 48–64 | Cite as

Effective Randomness of Unions and Intersections

Article

Abstract

We investigate the μ-randomness of unions and intersections of random sets under various notions of randomness corresponding to different probability measures. For example, the union of two relatively Martin-Löf random sets is not Martin-Löf random but is random with respect to the Bernoulli measure \(\lambda_{\frac{3}{4}}\) under which any number belongs to the set with probability \(\frac{3}{4}\). Conversely, any \(\lambda_{\frac{3}{4}}\) random set is the union of two Martin-Löf random sets. Unions and intersections of random closed sets are also studied.

Keywords

Computable analysis Computability Randomness 

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of FloridaGainesvilleUSA
  2. 2.Department of MathematicsDartmouth CollegeHanoverUSA

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