Benci, Vieri; Bottazzi, Emanuele; Di Nasso, Mauro Some applications of numerosities in measure theory. (English) Zbl 1309.26028 Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Nat., IX. Ser., Rend. Lincei, Mat. Appl. 26, No. 1, 37-47 (2015). Summary: We present some applications of the notion of numerosity to measure theory, including the construction of a non-Archimedean model for the probability of infinite sequences of coin tosses. Cited in 2 Documents MSC: 26E30 Non-Archimedean analysis 28E15 Other connections with logic and set theory 26E35 Nonstandard analysis 60A05 Axioms; other general questions in probability Keywords:non-Archimedean mathematics; measure theory; nonstandard analysis; numerosities PDFBibTeX XMLCite \textit{V. Benci} et al., Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Nat., IX. Ser., Rend. Lincei, Mat. Appl. 26, No. 1, 37--47 (2015; Zbl 1309.26028) Full Text: DOI arXiv References: [1] V. Benci, I numeri e gli insiemi etichettati, Conferenza del seminario di matematica dell’Universita‘ di Bari, vol. 261 (1995), Laterza, pp. 1-29. [2] V. Benci - E. Bottazzi - M. Di Nasso, Elementary numerosity and measures, J. Log. Anal., vol. 6 (2014). · Zbl 1300.26018 [3] V. Benci - M. Di Nasso, Numerosities of labelled sets: a new way of counting, Adv. Math., vol. 173 (2003), pp. 50-67. · Zbl 1028.03042 [4] V. Benci - M. Di Nasso, How to Measure the Infinite-The Theory of Alpha-Limits and the Numerosities, book in preparation. · Zbl 1429.26001 [5] V. Benci - M. Di Nasso - M. Forti, An Aristotelian notion of size, Ann. Pure Appl. Logic, vol. 143 (2006), pp. 43-53. · Zbl 1114.03055 [6] V. Benci - L. Horsten - S. Wenmackers, Non-Archimedean probability, Milan J. Math. vol. 81 (2013), pp. 121-151. [7] E. Bottazzi, W-Theory: Mathematics with Infinite and Infinitesimal Numbers (2012), Master thesis, University of Pavia (Italy). [8] M. Di Nasso - M. Forti, Numerosities of point sets over the real line, Trans. Amer. Math. Soc., vol. 362 (2010), pp. 5355-71. · Zbl 1200.03033 [9] J. Yeh, Real Analysis, Theory of Measure and Integration (2006), World Scientific Publishing Co. Pte. Ltd. · Zbl 1098.28002 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.