An Algorithmic Approach to Information Theory
Classical probability theory is based on the well known axioms of Kolmogoroff. A characteristic difficulty of this measure-theoretic approach is the physical interpretation of probability: we can observe only the frequency of events and the order in which they occur, not however the probability in the axiomatic sense. Attempts to formulate a frequency theory of probability are quite old, but it was not until the fundamental work of C.P. Schnorr (1971) that there existed a complete canonical theory of probability and randomness based on the concept of an effective (that is, computable) procedure to detect possible regularities in a sequence of events.
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