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Egoroff’s Theorem and Lusin’s Theorem for Capacities in the Framework of g‐Expectation
Mathematical Problems in Engineering, Volume 2020, Issue 1, 2020., 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 +3 more
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Intrinsic Square Function Characterizations of Variable Hardy–Lorentz Spaces
Journal of Function Spaces, Volume 2020, Issue 1, 2020., 2020 The aim of this paper is to establish the intrinsic square function characterizations in terms of the intrinsic Littlewood–Paley g‐function, the intrinsic Lusin area function, and the intrinsic gλ∗‐function of the variable Hardy–Lorentz space Hp(⋅),q(ℝn), for p(⋅) being a measurable function on ℝn satisfying 0
Khedoudj Saibi, Huy Qui Bui
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A C^k Lusin Approximation Theorem For Real-Valued Functions on Carnot Groups [PDF]
, 2022 We study the Lusin approximation problem for real-valued measurable functions on Carnot groups. We prove that k-approximate differentiability almost everywhere is equivalent to admitting a Lusin approximation by $C^{k}_{\mathbb{G}}$ maps.
Speight, Gareth +2 more
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Lusin’s theorem for derivatives with respect to a continuous function [PDF]
Proceedings of the American Mathematical Society, 1999 For a nowhere constant continuous function g g on a real interval
AVERSA, VINCENZO LIBERO, PREISS D.
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Structure of level sets and Sard-type properties of Lipschitz maps [PDF]
, 2013 We consider certain properties of maps of class C2 from Rd to Rd−1 that are strictly related to Sard’s theorem, and we show that some of them can be extended to Lipschitz maps, while others require some additional regularity.
Bianchini, S. +8 more
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Lusin's Theorem and Bochner Integration
, 2004 To appear in Scientiae Mathematicae ...
Loeb, Peter A., Talvila, Erik
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A lusin type theorem for gradients
Journal of Functional Analysis, 1991 The main result of the paper is the following: Theorem 1. Let \(\Omega\) be an open subset of \(\mathbb{R}^ N\) (\(N>1\)) with finite measure, and let \(f: \Omega\to\mathbb{R}^ N\) be a Borel function. Then, for every \(\varepsilon>0\), there exist an open set \(A\subset\Omega\) and a function \(u\in{\mathcal C}_ 0^ 1(\Omega)\) such that \(| A|\leq ...
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A Space with a Lusin $\pi$-Base Whose Square Has No Lusin $\pi$-Base
, 2021 We construct a space $X$ that has a Lusin $\pi$-base and such that $X^2$ has no Lusin $\pi$-base.
Mikhail Patrakeev
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A Note on Sobolev‐Lorentz Capacity and Hausdorff Measure
Mathematische Nachrichten, Volume 299, Issue 7, Page 1540-1548, July 2026.ABSTRACT In this paper, we give an elementary proof that sets of zero p,1$p,1$‐Sobolev‐Lorentz capacity are Hn−p$\mathcal {H}^{n-p}$‐null sets, independently of nonlinear potential theory. We further show that there exists a set of Sobolev‐Lorentz‐(p,1)$(p,1)$ capacity equal to zero with Hausdorff dimension equal n−p$n-p$.
Daniel Campbell
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Littlewood, Paley and almost‐orthogonality: a theory well ahead of its time
Journal of the London Mathematical Society, Volume 113, Issue 5, May 2026.Abstract The classic paper by Littlewood and Paley [J. Lond. Math. Soc. (1), 6 (1931), 230–233] marked the birth of Littlewood–Paley theory. We discuss this paper and its impact from a historical perspective, include an outline of the results in the paper and their subsequent significance in relation to developments over the last century, and set them ...
Anthony Carbery
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