Results 1 to 10 of about 85 (70)
Note on the Regularity of Nonadditive Measures [PDF]
Journal of Applied Mathematics, 2013 We consider the regularity for nonadditive measures. We prove that the non-additive measures which satisfy Egoroff's theorem and have pseudometric generating property possess Radon property (strong regularity) on a complete or a locally compact ...
Toshikazu Watanabe +2 more
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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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On the Independence of a Generalized Statement of Egoroff's Theorem from ZFC after T. Weiss
Real Analysis Exchange, 2007 6 ...
null Roberto Pinciroli
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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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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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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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On a singular anisotropic parabolic equation related to the p → ( x ) $\vec{p}(x)$ -Laplacian
Boundary Value ProblemsThis paper investigates a singular anisotropic parabolic equation associated with the p i ( x ) $p_{i}(x)$ -Laplacian operator. By employing the anisotropic Gagliardo-Sobolev-Nirenberg inequality and a modified Di Giorgi iteration technique, we derive a ...
Qitong Ou, Huashui Zhan
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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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An extension of Eegoroff’s and Lusin’s theorems in operator-valued case
Filomat, 2018 Here, we extend three basic facts from classical measure theory to operator-valued case. At first we show that operator-valued measurable functions may be approximated by simple ones. In the sequel, two fundamental theorems Egoroff and Lusin are extended in operator-valued case.
Bagheri-Bardi, G. A. +1 more
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The Egoroff Theorem for Operator-Valued Measures in Locally Convex Spaces
, 2011 The Egoroff theorem for measurable $\bold X$-valued functions and operator-valued measures $\bold m: Σ\to L(\bold X, \bold Y)$, where $Σ$ is a $σ$-algebra of subsets of $T \neq \emptyset$ and $\bold X$, $\bold Y$ are both locally convex spaces, is proved. The measure is supposed to be atomic and the convergence of functions is net.
Haluska, Jan, Hutnik, Ondrej
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