Fair infinite lotteries

This article discusses how the concept of a fair finite lottery can best be extended to denumerably infinite lotteries. Techniques and ideas from non-standard analysis are brought to bear on the problem.

[1]  John K. Truss Foundations of Mathematical Analysis , 1997 .

[2]  Mauro Di Nasso,et al.  Numerosities of point sets over the real line , 2010 .

[3]  Luc Lauwers,et al.  Purely Finitely Additive Measures are Non-Constructible Objects , 2010 .

[4]  Vieri Benci,et al.  An Aristotelian notion of size , 2006, Ann. Pure Appl. Log..

[5]  Timothy Williamson,et al.  How probable is an infinite sequence of heads , 2007 .

[6]  Massimo Marraffa,et al.  Philosophical Papers, vol. I , 1994 .

[7]  Vieri Benci,et al.  The eightfold path to Nonstandard Analysis , 2004 .

[8]  Richard C. Jeffrey,et al.  Studies in inductive logic and probability , 1971 .

[9]  Vieri Benci,et al.  Alpha-theory: An elementary axiomatics for nonstandard analysis , 2003 .

[10]  Paolo Mancosu,et al.  MEASURING THE SIZE OF INFINITE COLLECTIONS OF NATURAL NUMBERS: WAS CANTOR’S THEORY OF INFINITE NUMBER INEVITABLE? , 2009, The Review of Symbolic Logic.

[11]  A. Robinson Non-standard analysis , 1966 .

[12]  Alfréd Rényi,et al.  Foundations of Probability , 1971 .

[13]  Paul Bartha,et al.  Countable Additivity and the de Finetti Lottery , 2004, The British Journal for the Philosophy of Science.

[14]  Thomas Augustin,et al.  Foundations of Probability , 2011, International Encyclopedia of Statistical Science.

[15]  Shaughan Lavine Finite mathematics , 2005, Synthese.

[16]  K. Lempert,et al.  CONDENSED 1,3,5-TRIAZEPINES - IV THE SYNTHESIS OF 2,3-DIHYDRO-1H-IMIDAZO-[1,2-a] [1,3,5] BENZOTRIAZEPINES , 1983 .

[17]  B. M. Hill,et al.  Theory of Probability , 1990 .

[18]  A. Elga Infinitesimal Chances and the Laws of Nature , 2004 .

[19]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[20]  Péter Komjáth,et al.  Ultrafilters , 2008, Am. Math. Mon..

[21]  Hannes Leitgeb,et al.  Finitistic and Frequentistic Approximation of Probability Measures with or without σ-Additivity , 2008, Stud Logica.

[22]  Dudley,et al.  Real Analysis and Probability: Integration , 2002 .

[23]  Vieri Benci,et al.  An elementary approach to Stochastic Differential Equations using the infinitesimals , 2008, 0807.3477.

[24]  D. Lewis A Subjectivist’s Guide to Objective Chance , 1980 .

[25]  J. Kubilius,et al.  Probabilistic Methods in the Theory of Numbers , 1964 .

[26]  W. Luxemburg Non-Standard Analysis , 1977 .

[27]  S. Poirier Foundations of mathematics , 2007 .

[28]  J. E. Rubio Optimization and Nonstandard Analysis , 1994 .

[29]  Vieri Benci,et al.  Numerosities of labelled sets: a new way of counting , 2003 .

[30]  Nigel J. Cutland Nonstandard Measure Theory and its Applications , 1983 .

[31]  L. M. M.-T. Theory of Probability , 1929, Nature.

[32]  Andreas Blass,et al.  Ultrafilters across Mathematics , 2010 .

[33]  William S. Hatcher,et al.  Foundations of Mathematics , 1968 .