Abstract
Let us represent the successive outcomes of an experiment by a sequence of independent and identically distributed random variables on some probability space. Let us assume that these random variables will be binary valued taking the values 0 and 1. As it is well known, according to R. von Mises’ definition of randomness, the first condition for the existence of a random sequence (or Kollectiv) is that the limit of the relative frequencies of O’s and 1’s exist; the second requirement is that the limit frequence should remain invariant under place selection made by any countable set of place selection functions.
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References
Carsetti, A. (1981), “Semantica dei mondi possibili ed operatori iperintensionali”. In Atti del Convegno nazionale di Logica, edited by S. Bernini. Napoli: Bibliopolis.
Carsetti, A. (1982), “Semantica denotazionale e sistemi autopoietici”. La Nuova Critica 64: 51–91.
Chaitin, G. (1977), “Algorithmic entropy of sets”. Comp. and Math, with applications 2: 235–45.
Chaitin, G. (1987), Algorithmic Information Theory. Cambridge: Cambridge University Press.
Gaifman, H. and Snir, M. (1982), “Probabilities over rich languages, testing and randomness”. J. Symb. Logic 47: 495–548
Humphreys, P.W. (1977), “Randomness, Independence and Hypotheses”. Synthèse 36: 415–26.
Kolmogoroff, A.N. (1956), “Logical basis for information theory and probability”. IEEE Trans. Inf. Th. IT-14: 662–664.
Martin Löf, P. (1966), “The definition of random sequences”. Inf. and Control 9: 602–619.
Schnorr, C.P. (1971), “A unified approach to the definition of random sequences”. Math. Syst. Theory 5: 246–258.
Schnorr, C.P. (1974), Unpublished manuscript.
Scott, D. (1982), “Domains for Denotational Semantics”. In Automata, Languages and Programming, edited by Nielsen M. and Schmidt, E.M.: Berlin: Springer.
Solovay, R.M. (1975), Unpublished manuscript.
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© 1988 Kluwer Academic Publishers
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Carsetti, A. (1988). Probability, Randomness and Information. In: Agazzi, E. (eds) Probability in the Sciences. Synthese Library, vol 201. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3061-2_12
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DOI: https://doi.org/10.1007/978-94-009-3061-2_12
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