Results 1 to 10 of about 69 (48)
Egoroff's Theorem and the Distribution of Standard Points in a Nonstandard Model [PDF]
Proceedings of the American Mathematical Society, 1981 We study the relationship between the Loeb measure °(*fi) of a set £ and the /?-measure of the set S(E) = [x\*x G E) of standard points in E. If E is in the a-algebra generated by the standard sets, then °(*f0(£) — piS(Ef). This is used to give a short nonstandard proof of Egoroffs Theorem.
Henson, C. Ward, Wattenberg, Frank
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On the Independence of a Generalized Statement of Egoroff's Theorem from ZFC after T. Weiss
Real Analysis Exchange, 2007 6 ...
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Formalized Mathematics, 2008 In this paper n, k are natural numbers, X is a non empty set, and S is a σ-field of subsets of X. Next we state several propositions: (1) Let M be a σ-measure on S, F be a function from N into S, and given n. Then {x ∈ X: ∧ k (n ≤ k ⇒ x ∈ F (k))} is an element of S. (2) Let F be a sequence of subsets of X and n be an element of N.
Noboru Endou +2 more
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On Null-Continuity of Monotone Measures
Mathematics, 2020 The null-continuity of monotone measures is a weaker condition than continuity from below and possesses many special properties. This paper further studies this structure characteristic of monotone measures.
Jun Li
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Egoroff's theorems for random sets on non-additive measure spaces
AIMS Mathematics, 2021 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Tao Chen, Hui Zhang, Jun Li
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Egoroff’s Theorem and Lusin’s Theorem for Capacities in the Framework of
Mathematical Problems in Engineering, 2020 In the classical real analysis theory, Egoroff’s theorem and Lusin’s theorem are two of the most important theorems. The σ-additivity of measures plays a crucial role in the proofs of these theorems. Later, many researchers have carried out lots of studies on Egoroff’s theorem and Lusin’s theorem when the measure is monotone and nonadditive (see, e.g.,
Zhaojun Zong, Feng Hu, Xiaoxin Tian
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Egoroff’s theorem in measurable operator spaces associated with a Von Neumann algebra
Indian Journal of Pure and Applied Mathematics, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Shen, Congcong, Jiang, Lining
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