Results 31 to 40 of about 337,654 (135)
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 ...
openaire +3 more sources
Nonamenable subforests of multi‐ended quasi‐pmp graphs
Proceedings of the London Mathematical Society, Volume 133, Issue 3, September 2026.Abstract We prove the a.e. nonamenability of locally finite quasi‐pmp Borel graphs whose every component admits at least three nonvanishing ends with respect to the underlying Radon–Nikodym cocycle. We witness their nonamenability by constructing Borel subforests with at least three nonvanishing ends per component, and then applying Tserunyan and ...
Ruiyuan Chen +2 more
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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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Lusin spaces as images of locally compact Polish spaces [PDF]
, 2023 A Lusin space is a Hausdorff space being the image of a Polish space under a continuous bijection. Such spaces have multiple applications, in particular, as state spaces of various stochastic systems.
Kargol, Alina, Kozitsky, Yuri
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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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A radial uniqueness theorem for meromorphic functions
, 1982 A classical theorem of Lusin and Privalov states that a meromorphic function in the unit disc, which has radial limit zero on a set which is both of second category and metrically dense in some boundary arc, must vanish identically.
P. J. Rippon
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Exactness and the topology of the space of invariant random equivalence relations
Proceedings of the London Mathematical Society, Volume 132, Issue 5, May 2026.Abstract We characterize exactness of a countable group Γ$\Gamma$ in terms of invariant random equivalence relations (IREs) on Γ$\Gamma$. Specifically, we show that Γ$\Gamma$ is exact if and only if every weak limit of finite IREs is an amenable IRE.
Héctor Jardón‐Sánchez +3 more
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Abstract and Applied Analysis, Volume 2016, Issue 1, 2016., 2016 We construct a continuous function f:[0,1]→R such that f possesses N−1‐property, but f does not have approximate derivative on a set of full Lebesgue measure. This shows that Banach’s Theorem concerning differentiability of continuous functions with Lusin’s property (N) does not hold for N−1‐property. Some relevant properties are presented.
Stanisław Kowalczyk +2 more
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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. +7 more
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A Choquet theory of Lipschitz‐free spaces
Proceedings of the London Mathematical Society, Volume 132, Issue 2, February 2026.Abstract Let (M,d)$(M,d)$ be a complete metric space and let F(M)$\mathcal {F}({M})$ denote the Lipschitz‐free space over M$M$. We develop a ‘Choquet theory of Lipschitz‐free spaces’ that draws from the classical Choquet theory and the De Leeuw representation of elements of F(M)$\mathcal {F}({M})$ (and its bi‐dual) by positive Radon measures on βM ...
Richard J. Smith
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