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- date : 2015-05-20 01:10|hit : 1778
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- Article] Non-Archimedean Probability
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DocNo of ILP: 648
Doc. Type: Article
Title: Non-Archimedean Probability
Authors: Benci, V; Horsten, L; Wenmackers, S
Full Name of Authors: Benci, Vieri; Horsten, Leon; Wenmackers, Sylvia
Keywords by Author: Probability; axioms of Kolmogorov; nonstandard models; fair lottery; non-Archimedean fields
Keywords Plus: CONDITIONAL-PROBABILITY; NONSTANDARD; SEQUENCE; HEADS; SETS
Abstract: We propose an alternative approach to probability theory closely related to the framework of numerosity theory: non-Archimedean probability (NAP). In our approach, unlike in classical probability theory, all subsets of an infinite sample space are measurable and only the empty set gets assigned probability zero (in other words: the probability functions are regular). We use a non-Archimedean field as the range of the probability function. As a result, the property of countable additivity in Kolmogorov's axiomatization of probability is replaced by a different type of infinite additivity.
Cate of OECD: Mathematics
Year of Publication: 2013
Business Area: lottery
Detail Business: lottery
Country: Switzerland
Study Area:
Name of Journal: MILAN JOURNAL OF MATHEMATICS
Language: English
Country of Authors: [Benci, Vieri] Univ Pisa, Dipartimento Matemat Applicata, I-56127 Pisa, Italy; [Benci, Vieri] King Saud Univ, Coll Sci, Dept Math, Riyadh 11451, Saudi Arabia; [Horsten, Leon] Univ Bristol, Dept Philosophy, Bristol BS8 1UU, Avon, England; [Wenmackers, Sylvia] Univ Groningen, Fac Philosophy, NL-9712 GL Groningen, Netherlands
Press Adress: Benci, V (reprint author), Univ Pisa, Dipartimento Matemat Applicata, Via F Buonarroti 1-C, I-56127 Pisa, Italy.
Email Address: benci@dma.unipi.it; leon.horsten@bristol.ac.uk; s.wenmackers@rug.nl
Citaion:
Funding:
Lists of Citation: Bartha P, 1999, SYNTHESE, V118, P403, DOI 10.1023/A:1005100407551; Benci V, 2003, EXPO MATH, V21, P355, DOI 10.1016/S0723-0869(03)80038-5; Benci V., 2012, INFINITESIMAL UNPUB; Benci V., 2006, LECT NOTES LOGIC, V25, P3; Benci V, 2006, ANN PURE APPL LOGIC, V143, P43, DOI 10.1016/j.apal.2006.01.008; Benci V., 1995, C SEM MAT U BAR BAR, V261, P29; Benci V, 2003, ADV MATH, V173, P50, DOI 10.1016/S0001-8708(02)00012-9; Bottazzi E., 2012, THESIS U PAVIA ITALY; CUTLAND NJ, 1983, B LOND MATH SOC, V15, P529, DOI 10.1112/blms/15.6.529; de Finetti B., 1974, PROBABILITY; Gilbert T., 1996, CAHIERS CTR LOGIQUE, V9, P99; Hajek A, 2003, SYNTHESE, V137, P273, DOI 10.1023/B:SYNT.0000004904.91112.16; Kadane J. B., 1986, BAYESIAN INFERENCE D; Keisler H. J., 2002, LECT NOTES LOGIC; Keisler H. J., 2011, FDN INFINITESIMAL CA; Kolmogorov A. N., 1956, ERGEBNISSE MATH, V1933; LEVI I, 1978, THEOR DECIS, V9, P1, DOI 10.1007/BF00138117; Lewis D. K., 1980, STUDIES INDUCTIVE LO, P263; LOEB PA, 1975, T AM MATH SOC, V211, P113, DOI 10.2307/1997222; Nelson E., 1987, RADICALLY ELEMENTARY; Skyrms Brian, 1980, CAUSAL NECESSITY; Weintraub R, 2008, ANALYSIS-UK, V68, P247, DOI 10.1111/j.1467-8284.2008.00747.x; Wenmackers S., 2010, SYNTHESE IN PRESS, DOI [10.1007/s11229-010-9836-x, DOI 10.1007/S11229-010-9836-X]; Williamson T, 2007, ANALYSIS, V67, P173, DOI 10.1111/j.1467-8284.2007.00671.x
Number of Citaion: 24
Publication: SPRINGER BASEL AG
City of Publication: BASEL
Address of Publication: PICASSOPLATZ 4, BASEL, 4052, SWITZERLAND
ISSN: 1424-9286
29-Character Source Abbreviation: MILAN J MATH
ISO Source Abbreviation: Milan J. Math.
Volume: 81
Version: 1
Start of File: 121
End of File: 151
DOI: 10.1007/s00032-012-0191-x
Number of Pages: 31
Web of Science Category: Mathematics, Applied; Mathematics
Subject Category: Mathematics
Document Delivery Number: 135JM
Unique Article Identifier: WOS:000318284400006
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