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Lusin-type theorem for functions with prescribed gradient

In the first part of this thesis we discuss and prove a theorem by Giovanni Alberti whose statement shares similarities to that of Lusin's Theorem, hence the "Lusin-type theorem" definition. The theorem states that given a Borel vector field f on a finite measure set and some epsilon greater than zero, it is always possible to find a set of measure ...
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Extensions of the Lusin's Theorem, the Severini-Egorov's Theorem and the Riesz Subsequence Theorems

Asian Research Journal of Mathematics, 2016
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Egoroff’s theorem and Lusin’s theorem for complex uncertain sequences

Journal of Intelligent & Fuzzy Systems, 2022
Complex 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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Lusin's theorem on fuzzy measure spaces

Fuzzy Sets and Systems, 2004
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Jun Li 0014, Masami Yasuda
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Lusin's theorem on monotone measure spaces

Fuzzy Sets and Systems, 2011
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Jun Li 0014, Radko Mesiar
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A Remark on the Theorems of Lusin and Egoroff

Canadian Mathematical Bulletin, 1964
In 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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On Lusin’s Theorem for Non-additive Measure

2011
In this paper, we prove Lusin’s theorem remains valid for nonadditive Borel measure under the conditions of weakly null additivity, continuity from above and a certain additional continuity.
Tamaki Tanaka, Toshikazu Watanabe
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Proof of a theorem of Lusin

Mathematical Notes of the Academy of Sciences of the USSR, 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.
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A Lusin theorem for a class of Choquet capacities

Statistical Papers, 2002
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Castaldo, Adriana, Marinacci, Massimo
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The Theorems of Lusin and Egoroff

1971
A real-valued function f on R is called measurable if f−1(U) is measurable for every open set U in R. f is said to have the property of Baire if f −1 (U) has the property of Baire for every open set U in R. In either definition, U may be restricted to some base, or allowed to run over all Borel sets.
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