On-line Randomness

The first on-line definition of randomness was due to Claus-Peter Schnorr; an equivalent definition was given by Leonid Levin. Both of them showed that their definitions (for Schnorr, one of several definitions that he proposed) are equivalent to the standard definition due to Martin-Lof.

Versions of Schnorr's definition that respect Dawid's prequential principle are being studied by Shen, Alexey Chernov, Vereshchagin, and Volodya Vovk.

Open problems: to appear.