Natural density and probability, constructively

Samuele Maschio

Abstrakt

We give a constructive account of the frequentist approach to probability, by means of natural density. Then we discuss some probabilistic variants of the Limited Principle of Omniscience.

AMS Subject Classification: 03F65, 60A05.

Słowa kluczowe: constructive probability, frequentist probability, natural density, limited principle of omniscience.
References

[1] E. Bishop, D. S. Bridges, Constructive analysis, Springer 1985.

[2] D. Bridges, F. Richman, Varieties of Constructive Mathematics, Cambridge University Press 1987.

[3] Y.K. Chan, Notes on constructive probability theory, Ann. Probability 2 (1974), 51-75

[4] H. Ishihara, Reverse Mathematics in Bishop’s Constructive Mathematics, Philosophia Scientae (2006), 43–59.

[5] M.E. Maietti, A minimalist two-level foundation for constructive mathematics, Annals of Pure and Applied Logic 160:3 (2009), 319–354.

[6] M.E. Maietti, G. Sambin, Toward a minimalist foundation for constructive mathematics, In: From Sets and Types to Topology and Analysis: Practicable Foundations for Constructive Mathematics (Eds. L. Crosilla, P. Schuster), Oxford University Press 2005, pp. 91–114.

[7] I. Niven, The asymptotic density of sequences, Bull. Amer. Math. Soc. 6:11 (1951), 420–434

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