74 citations · 75 across the 5 of their papers we have counts for
6 papers
The universal measure of probabilistically nonrandom objects
Vladimir Vovk
A finite object is called probabilistically random if it is an algorithmically random element of a finite set whose Kolmogorov complexity is relatively small. This note studies the…
The universal measure of nonstochastic objects
Vladimir Vovk
The usual settings for discussing the notion of stochasticity are very different from Kolmogorov's original setting as recorded by Shen in November 1981. This paper simplifies Kolm…
The non-mathematical section of Kolmogorov's Grundbegriffe
Vladimir Vovk
Kolmogorov's "Grundbegriffe der Wahrscheinlichkeitsrechnung" introduced the standard measure-theoretic formalization of probability but included only a two-page section about the r…
A Conversation with A. Philip Dawid
Vladimir Vovk, Glenn Shafer
Beginning in the 1970s, Alexander Philip Dawid has been a leading contributor to the foundations of statistics and especially to the development and application of Bayesian statist…
Levy's zero-one law in game-theoretic probability
Glenn Shafer, Vladimir Vovk, Akimichi Takemura
We prove a game-theoretic version of Levy's zero-one law, and deduce several corollaries from it, including non-stochastic versions of Kolmogorov's zero-one law, the ergodicity of…
The Sources of Kolmogorov's Grundbegriffe
Glenn Shafer, Vladimir Vovk
Andrei Kolmogorov's Grundbegriffe der Wahrscheinlichkeits-rechnung put probability's modern mathematical formalism in place. It also provided a philosophy of probability--an explan…