# Infinitesimals are too small for countably infinite fair lotteries

Article

First Online:

- 260 Downloads
- 4 Citations

## Abstract

We show that infinitesimal probabilities are much too small for modeling the individual outcome of a countably infinite fair lottery.

## Keywords

Probability Infinity Infinitesimals Regularity## References

- Bernstein, A. R., & Wattenberg, F. (1969). Non-standard measure theory. In W. A. J. Luxemberg (Ed.),
*Applications of model theory of algebra, analysis, and probability*. New York: Holt, Rinehart and Winston.Google Scholar - Corbae, D., Stinchcombe, M. B., & Zeman, J. (2009).
*An introduction to mathematical analysis for economic theory and econometrics*. Princeton: Princeton University Press.Google Scholar - Elga, A. (2004). Infinitesimal chances and the laws of nature.
*Australasian Journal of Philosophy*,*82*, 67–76.CrossRefGoogle Scholar - Hájek, A. (2011).
*Staying regular?*. In Australasian Association of Philosophy Conference.Google Scholar - Kadane, J. B., Schervish, M. J., & Seidenfeld, T. (1996). Reasoning to a foregone conclusion.
*Journal of the American Statistical Association*,*91*, 1228–1235.CrossRefGoogle Scholar - Mourges, M. H., & Ressayre, J. P. (1993). Every real closed field has an integer part.
*Journal of Symbolic Logic*,*58*, 641–647.CrossRefGoogle Scholar - Pedersen, A.P. (2012). Impossibility results for any theory of non-Archimedean expected value (manuscript).Google Scholar
- Pruss, A. R. (2012). Infinite lotteries, perfectly thin darts and infinitesimals.
*Thought*,*1*, 81–89.Google Scholar - Schervish, M. J., Seidenfeld, T., & Kadane, J. B. (1984). The extent of non-conglomerability of finitely additive probabilities.
*Probability Theory and Related Fields*,*66*, 205–226.Google Scholar - Wenmackers, S., & Horsten, L. (2013). Fair infinite lotteries, Synthese,
*190*(1), 37–61.Google Scholar

## Copyright information

© Springer Science+Business Media Dordrecht 2013