A CHARACTERIZATION OF INFINITE BINARY SEQUENCES WITH PARTIAL RANDOMNESS

K-randomness and Martin-Lof randomness are among many formalizations o f randomness of infinite sequences, and these two are known to be equi valent. We can naturally modify the former to the definition of partia l randomness. However, it is not obvious how to modify the latter to t he definition of partial randomness. In this paper, we show that we ca n modify Martin-Lof randomness to a definition of partial randomness t hat is equivalent to the definition obtained by naturally modifying K- randomness. The basic idea is to modify the notion of measures used in the definition of Martin-Lof tests.