2011/03/17 by Peter G. Doyle, Doyle, Peter G.
Mathematics · #03D32 #03E45 #60A05 #FOS: Mathematics #Logic (math.LO) #Probability (math.PR) #math.LO #math.PR #msc:03D32 #msc:03E45 #msc:60A05
paper · pdf · doi:10.48550/arxiv.1103.3494
Public domain - no copyright
arxiv created 2011/03/17 · arxiv updated 2011/03/18
An infinite binary sequence is deemed to be random if it has all definable properties that hold almost surely for the usual probability measure on the set of infinite binary sequences. There are only countably many such properties, so it would seem that the set of random sequences should have full measure. But in fact there might be no random sequences, because for all we know, there might be no undefinable sets.