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Lusin's theorem on fuzzy measure spaces
Fuzzy Sets and Systems, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Masami Yasuda
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Lusin's theorem on monotone measure spaces
Fuzzy Sets and Systems, 2011zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Radko Mesiar
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On a Theorem of Banach and Kuratowski and $K$-Lusin Sets
Rocky Mountain Journal of Mathematics, 2003 In a paper of 1929, Banach and Kuratowski proved, assuming the continuum hypothesis, a combinatorial theorem which implies that there is no non-vanishing sigma-additive finite measure on the real line which is defined for every set of reals. It will be shown that the combinatorial theorem is equivalent to the existence of a K-Lusin set of size the ...
Lorenz J. Halbeisen, Tomek Bartoszyński
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Egoroff’s theorem and Lusin’s theorem for complex uncertain sequences
Journal of Intelligent & Fuzzy Systems, 2022Complex uncertain variables are measurable functions from uncertainty spaces to the set of complex numbers and are used to model complex uncertain quantities. In this paper, we investigate Egoroff’s theorem and Lusin’s theorem for complex uncertain sequences. For studying these theorems, we introduce two concepts: strongly order continuous and regular.
Yu Tian, Zhaojun Zong, Feng Hu 0002
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Mathematical Notes, 1978
In [1, 2], Lusin published a theorem (with proof) asserting that a very simple set constructed by him is not Borel. Lunina [3] discovered an error in Lusin's proof. It is proved that Lusin's theorem is nonetheless valid.
Vladimir Kanovei
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In [1, 2], Lusin published a theorem (with proof) asserting that a very simple set constructed by him is not Borel. Lunina [3] discovered an error in Lusin's proof. It is proved that Lusin's theorem is nonetheless valid.
Vladimir Kanovei
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Journal of Mathematical Analysis and Applications, 2017 In this paper we consider a general d-dimensional second-order elliptic Partial Differential Equation (PDE) with variable coefficients, and we extend previous results on the spectral distribution of discretization matrices arising from B-spline ...
Stefano Serra Capizzano +2 more
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A Quantitative Lusin Theorem for Functions in BV [PDF]
Springer INdAM Series, 2015 We extend to the BV case a measure theoretic lemma previously proved by DiBenedetto et al. (Atti Accad. Naz. Lincei Cl. Sci. Mat. Appl. 9, 223–225, 2006) in W loc 1, 1. It states that if the set where u is positive occupies a sizable portion of an open set E then the set where u is positive clusters about at least one point of E. In this note we follow
Vincenzo Vespri, András Telcs
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ON LUSIN'S THEOREM IN THE ASPECT OF SMALL SYSTEMS
Demonstratio Mathematica, 1995 Let \(S\) be a \(\sigma\)-algebra of subsets of a set \(X\). By a small system a sequence of families \((N_n)_n\subset S\) satisfying some axioms is understood. If \(m\) is a positive measure, then the family \(N_n\) of all sets of a measure less than \(1/n\) can serve as an example.
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A Remark on the Theorems of Lusin and Egoroff
Canadian Mathematical Bulletin, 1964In this note we do not intend to establish new results but only to suggest a very simple proof of Lusin's theorem, direct for σ-finite regular measures, a proof that bypasses the usual procedure of first establishing this theorem for sets of finite measure only.
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