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Finitely Additive Equivalent Martingale Measures [PDF]
Journal of Theoretical Probability, 2010 Let L be a linear space of real bounded random variables on the probability space (omega,A, P0). There is a finitely additive probability P on A, such that P tilde P0 and EP (X) = 0 for all X in L, if and only if cEQ(X) = ess sup(-X), X in L, for some ...
Luca Pratelli +2 more
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On Finitely Additive Vector Measures [PDF]
Proceedings of the National Academy of Sciences, 1970 In this paper we extend the well-known Vitali-Hahn-Saks and Nikodým theorems for measures to finitely additive vector-valued set functions.
Brooks, J. K., Jewett, R. S.
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On the Additive Property of Finitely Additive Measures [PDF]
Journal of Theoretical Probability, 2021 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On projections of finitely additive measures [PDF]
Proceedings of the American Mathematical Society, 1979 A theorem of Z. Frolík and M. E. Rudin states that for every two-valued measure μ \mu on N, if F : N → N F:N \to N is such that F ∗ ( μ ) = μ {F_ \ast }(\mu ) = \mu then
Jech, Thomas, Prikry, Karel
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Finitely-additive, countably-additive and internal probability measures [PDF]
Commentationes Mathematicae Universitatis Carolinae, 2019 We discuss two ways to construct standard probability measures, called push-down measures, from internal probability measures. We show that the Wasserstein distance between an internal probability measure and its push-down measure is infinitesimal. As an application to standard probability theory, we show that every finitely-additive Borel probability ...
Duanmu, Haosui, Weiss, William
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Finitely Additive Gleason Measures [PDF]
Proceedings of the American Mathematical Society, 1992 We describe the set of all finitely additive measures which attain also infinite values on a quantum logic of a Hilbert space and which are expressible via the generalized Gleason-Lugovaja-Sherstnev formula. We prove that this set consists of those which are regular with respect to the set of all finite-dimensional subspaces.
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The Hausdorff moment problem under finite additivity [PDF]
, 2007 We investigate to what extent finitely additive probability measures on the unit interval are determined by their moment sequence. We do this by studying the lower envelope of all finitely additive probability measures with a given moment sequence.
De Cooman, Gert +2 more
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Convergence in measure under finite additivity [PDF]
Sankhya A, 2013 We investigate the possibility of replacing the topology of convergence in probability with convergence in $L^1$. A characterization of continuous linear functionals on the space of measurable functions is also obtained.
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, 2016 A functional is said to be maxitive if it commutes with the (pointwise) supremum operation. Such functionals find application in particular in decision theory and related fields.
Cattaneo, Marco E. G. V.
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Clarification of some mathematical misunderstandings about Savage's foundations of statistics, 1954 [PDF]
, 1993 This note discusses some mathematical misunderstandings about Savage (1954). It is shown that in his model the probability measure cannot be countably additive, that the set of events must be a σ-algebra and not just an algebra, that Savage did not ...
Wakker, P.P. (Peter)
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