Hyperreal-Valued Probability Measures Approximating a Real-Valued Measure

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Notre Dame Journal of Formal Logic 57 (3):369-374 (2016)
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Abstract

We give a direct and elementary proof of the fact that every real-valued probability measure can be approximated—up to an infinitesimal—by a hyperreal-valued one which is regular and defined on the whole powerset of the sample space.

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10.1215/00294527-3542210

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Author Profiles

Ralf Schindler
Thomas Hofweber
University of North Carolina, Chapel Hill

Citations of this work

Chance and the Continuum Hypothesis.Daniel Hoek - 2021 - Philosophy and Phenomenological Research 103 (3):639-60.
Hyperintensionality and Normativity.Federico L. G. Faroldi - 2019 - Cham, Switzerland: Springer Verlag.
Infinitesimal Probabilities.Sylvia Wenmackers - 2016 - In Richard Pettigrew & Jonathan Weisberg (eds.), The Open Handbook of Formal Epistemology. PhilPapers Foundation. pp. 199-265.
Cardinality Arguments Against Regular Probability Measures.Thomas Hofweber - 2014 - Thought: A Journal of Philosophy 3 (2):166-175.

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References found in this work

Non-Archimedean Probability.Vieri Benci, Leon Horsten & Sylvia Wenmackers - 2013 - Milan Journal of Mathematics 81 (1):121-151.
Nonstandard Measure Theory and its Applications.Nigel J. Cutland - 1983 - Journal of Symbolic Logic 54 (1):290-291.

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