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How NOT to Build an Infinite Lottery Machine

Norton, John D. (2019) How NOT to Build an Infinite Lottery Machine. [Preprint]

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Abstract

The sustained failure of efforts to design an infinite lottery machine using ordinary probabilistic randomizers is traced back to a problem familiar to set theorists: we have no constructive prescriptions for probabilistically non- measurable sets. Yet construction of such sets is required if we are to be able to read the result of an infinite lottery machine that is built from ordinary probabilistic randomizers. All such designs face a dilemma: they can provide an accessible (readable) result with probability zero; or an inaccessible result with probability greater than zero.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Norton, John D.jdnorton@pitt.edu0000-0003-0936-5308
Keywords: axiom of choice, non-constructible, infinite lottery, probability,
Subjects: Specific Sciences > Mathematics
Specific Sciences > Probability/Statistics
Depositing User: John Norton
Date Deposited: 19 Jul 2019 01:46
Last Modified: 19 Jul 2019 01:46
Item ID: 16236
Subjects: Specific Sciences > Mathematics
Specific Sciences > Probability/Statistics
Date: 14 July 2019
URI: http://philsci-archive.pitt.edu/id/eprint/16236

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