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On Finitely Additive Measures in Boolean Algebras. [PDF]
crll, 1964 © 1964 Walter de Gruyter GmbH. eingagen 20. April 1963. Part of this work was supported by National Science Foundation G-19914.
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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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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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Ultrafilter limits and finitely additive probability [PDF]
, 1982 Ultrafilter limits provide the natural convergence notion for finitely additive probability. The finitely additive infinitely divisible laws are closed under ultrafilter limits.
Sibley, Thomas Q.
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International Journal of Mathematics and Mathematical Sciences, 1993 By an Alexandrov lattice we mean a δ normal lattice of subsets of an abstract set X, such that the set of ℒ-regular countably additive bounded measures is sequentially closed in the set of ℒ-regular finitely additive bounded measures on the algebra ...
Albert Gorelishvili
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A Survey on Valdivia Open Question on Nikodým Sets
Mathematics, 2022 Let A be an algebra of subsets of a set Ω and ba(A) the Banach space of bounded finitely additive scalar-valued measures on A endowed with the variation norm. A subset B of A is a Nikodým set for ba(A) if each countable B-pointwise bounded subset M of ba(
Salvador López-Alfonso +3 more
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The Foundations of Probability with Black Swans
Journal of Probability and Statistics, 2010 We extend the foundation of probability in samples with rare events that are potentially catastrophic, called black swans, such as natural hazards, market crashes, catastrophic climate change, and species extinction. Such events are generally treated as ‘
Graciela Chichilnisky
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On Four Classical Measure Theorems
Mathematics, 2021 A subset B of an algebra A of subsets of a set Ω has property (N) if each B-pointwise bounded sequence of the Banach space ba(A) is bounded in ba(A), where ba(A) is the Banach space of real or complex bounded finitely additive measures defined on A ...
Salvador López-Alfonso +2 more
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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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The Topological Pressure of Linear Cellular Automata
Entropy, 2009 This elucidation studies ergodicity and equilibrium measures for additive cellular automata with prime states. Additive cellular automata are ergodic with respect to Bernoulli measure unless it is either an identity map or constant.
Chih-Hung Chang, Jung-Chao Ban
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