Results 21 to 30 of about 475 (237)
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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Smoothness conditions on measures using Wallman spaces
International Journal of Mathematics and Mathematical Sciences, 1999 In this paper, X denotes an arbitrary nonempty set, ℒ a lattice of subsets of X with ∅,X∈ℒ,A(ℒ) is the algebra generated by ℒ and M(ℒ) is the set of nontrivial, finite, and finitely additive measures on A(ℒ), and MR(ℒ) is the set of elements of M(ℒ ...
Charles Traina
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On Lebesgue-like Extensions of Finitely Additive Measures
Annals of Probability, 1974 Lester E Dubins
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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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On maximal measures with respect to a lattice
International Journal of Mathematics and Mathematical Sciences, 1991 Outer measures are used to obtain measures that are maximal with respect to a normal lattice. Alternate proofs are then given extending the measure theoretic characterizations of a normal lattice to an arbitrary, non-negative finitely additive measure on
James Camacho
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Measures on coallocation and normal lattices
International Journal of Mathematics and Mathematical Sciences, 1992 Let ℒ1 and ℒ2 be lattices of subsets of a nonempty set X. Suppose ℒ2 coallocates ℒ1 and ℒ1 is a subset of ℒ2. We show that any ℒ1-regular finitely additive measure on the algebra generated by ℒ1 can be uniquely extended to an ℒ2-regular measure on the ...
Jack-Kang Chan
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The Kullback–Leibler Information Function for Infinite Measures
Entropy, 2016 In this paper, we introduce the Kullback–Leibler information function ρ ( ν , μ ) and prove the local large deviation principle for σ-finite measures μ and finitely additive probability measures ν.
Victor Bakhtin, Edvard Sokal
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A note on invariant finitely additive measures [PDF]
Proceedings of the American Mathematical Society, 1985 We show that under certain general conditions any finitely additive measure which is defined for all subsets of a set X X ...
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Translation invariance and finite additivity in a probability measure on the natural numbers
International Journal of Mathematics and Mathematical Sciences, 2002 Inspired by the two envelopes exchange paradox, a finitely additive probability measure m on the natural numbers is introduced. The measure is uniform in the sense that m({i})=m({j}) for all i,j∈ℕ.
Robert Gardner, Robert Price
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An isomorphism theorem for finitely additive measures [PDF]
Proceedings of the American Mathematical Society, 1955 A problem which is appealing to the intuition in view of the relative frequency interpretation of probability is to define a measure on a countable space which assigns to each point the measure 0. Such a measure of course becomes trivial if it is countably additive. Finitely additive measures of this type have been discussed by R. C. Buck [I] and by E.
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