Eine Bemerkung zum Begriff der zufÄlligen Folge

SummaryMartin-Löf has defined random sequences to be those sequences which withstand a certain universal stochasticity test. On the other hand one can define a sequence to be random if it is not contained in any species of measure zero in the sense of Brouwer. Both definitions imply that these random sequences possess all statistical properties which can be checked by algorithms. We draw a comparison between the two concepts of constructive null sets and prove that they induce concepts of randomness which are not equivalent. The union of all species of measure zero in the sense of Brouwer is a proper subset of the universal constructive null set defined by Martin-Löf.