Effective Randomness of Unions and Intersections
We investigate the ?-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-Lf random sets is not Martin-Lf 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-Lf random sets. Unions and intersections of random closed sets are also studied.
randomness computable analysis computability