Random Closed Sets

Abstract

We investigate notions of randomness in the space C[2] of nonempty closed subsets of {0, 1}. A probability measure is given and a version of the Martin-Löf Test for randomness is defined. Π 2 random closed sets exist but there are no random Π 1 closed sets. It is shown that a random closed set is perfect, has measure 0, and has no computable elements. A… (More)
DOI: 10.1007/11780342_6

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