Fair infinite lotteries

Bartha P. (2004) Countable additivity and the de Finetti lottery. British Journal for the Philosophy of Science 55: 301–321CrossRefGoogle Scholar

Benci V., Di Nasso M. (2003a) Alpha-theory: An elementary axiomatic for nonstandard analysis. Expositiones Mathematicae 21: 355–386CrossRefGoogle Scholar

Benci V., Di Nasso M. (2003b) Numerosities of labelled sets: A new way of counting. Advances in Mathematics 173: 50–67CrossRefGoogle Scholar

Benci V., Di Nasso M., Forti M. (2006) The eightfold path to nonstandard analysis. In: Cutland N. J., Di Nasso M., Ross D. A. (eds) Nonstandard methods and applications in mathematics, Lecture notes in logic. Association for Symbolic Logic, AK Peters, Helsinki, pp 3–44Google Scholar

Benci, V., Galatolo, S. & Ghimenti, M. (2008). An elementary approach to stochastic differential equations using infinitesimals. Unpublished manuscript; http://arxiv.org/abs/0807.3477.

Cutland N. (1983) Nonstandard measure theory and its applications. Bulletin of the London Mathematical Society 15: 529–589CrossRefGoogle Scholar

de Finetti B. (1974) Theory of probability, Vols. 1 & 2 (A. Machí. Wiley, New YorkGoogle Scholar

Douven I., Horsten L., Romeijn J.-W. (2010) Probabilist anti-realism. Pacific Philosophical Quarterly 91: 38–63CrossRefGoogle Scholar

Dudley R. M. (2004) Real analysis and probability. Cambridge University Press, CambridgeGoogle Scholar

Easwaran, K. (2010). Regularity and infinitesimal credences. Unpublished manuscript.Google Scholar

Elga A. (2004) Infinitesimal chances and the laws of nature. Australasian Journal of Philosophy 82: 67–76CrossRefGoogle Scholar

Hájek, A. (2010). Staying regular. Unpublished manuscript.Google Scholar

Kolmogorov, A. N. (1933). Grundbegriffe der Wahrscheinlichkeitrechnung. (Ergebnisse Der Mathematik.) Foundations of probability. (2nd ed.) (N. Morrison, Trans., 1956). USA: Chelsea Publishing Company.Google Scholar

Komjáth P., Totik V. (2008) Ultrafilters. American Mathematical Monthly 115: 33–44Google Scholar

Lauwers, L. (2010). Purely finitely additive measures are non-constructible objects. Working paper, unpublished. Retrieved: May 29, 2010, from http://www.econ.kuleuven.be/ces/discussionpapers/Dps10/DPS1010.pdf.

Lavine S. (1995) Finite mathematics. Synthese 103: 389–420CrossRefGoogle Scholar

Lewis D. (1980) A subjectivist’s guide to objective chance. In: Jeffrey R. (eds) Studies in inductive logic and probability II. University of California Press, CaliforniaGoogle Scholar

Lewis D. (1986) Philosophical papers. Oxford University Press, OxfordGoogle Scholar

Mancosu P. (2009) Measuring the size of infinite collections of natural numbers. The Review of Symbolic Logic 2: 612–646CrossRefGoogle Scholar

McCall S., Armstrong D. M. (1989) God’s lottery. Analysis 49: 223–224Google Scholar

Ramsey F. P. (1926) Truth and probability. In: Braithwaite R. B. (eds) Foundations of mathematics and other essays. Routledge & P. Kegan, London, pp 156–198Google Scholar

Robinson A. (1966) Non-standard analysis. North-Holland Publishing Company, New YorkGoogle Scholar

Rubio J. E. (1994) Optimization and nonstandard analysis. Marcel Dekker, New YorkGoogle Scholar

Schurz G., Leitgeb H. (2008) Finitistic and frequentistic approximation of probability measures with or without σ-additivity. Studia Logica 89: 257–283CrossRefGoogle Scholar

Skyrms B. (1980) Causal Necessity. Yale University Press, New HavenGoogle Scholar

Tenenbaum G. (1995) Introduction to analytic and probabilistic number theory. Cambridge University Press, CambridgeGoogle Scholar

Truss J. (1997) Foundations of mathematical analysis. Clarendon Press, OxfordGoogle Scholar

Väth M. (2007) Nonstandard analysis. Springer, BerlinGoogle Scholar

Williamson T. (2007) How probable is an infinite sequence of heads?. Analysis 67: 173–180Google Scholar