Results 1 to 10 of about 76 (75)
Abstract and Applied Analysis, 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.
Stanisław Kowalczyk +1 more
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Variations on Lusin's Theorem [PDF]
Transactions of the American Mathematical Society, 1987 We prove a theorem about continuous restrictions of Marczewski measurable functions to large sets. This theorem is closely related to the theorem of Lusin about continuous restrictions of Lebesgue measurable functions to sets of positive measure and the theorem of Nikodým and Kuratowski about continuous restrictions of functions with the Baire property
Brown, Jack B., Prikry, Karel
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On a Lusin theorem for capacities [PDF]
Proceedings of the American Mathematical Society, 2021 Let X X be a compact metric space and let v v be a sub-additive capacity defined on X X . We show that Lusin’s theorem with respect to v v holds if and only if v v is continuous from above.
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On a geometric combination of functions related to Prékopa–Leindler inequality
Mathematika, Volume 69, Issue 2, Page 482-507, April 2023., 2023 Abstract We introduce a new operation between nonnegative integrable functions on Rn$\mathbb {R}^n$, that we call geometric combination; it is obtained via a mass transportation approach, playing with inverse distribution functions. The main feature of this operation is that the Lebesgue integral of the geometric combination equals the geometric mean ...
Graziano Crasta, Ilaria Fragalà
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Journal of Function Spaces, Volume 2023, Issue 1, 2023., 2023 Let L = −Δ + V be a Schrödinger operator on ℝn, where Δ denotes the Laplace operator ∑i=1n∂2/∂xi2 and V is a nonnegative potential belonging to a certain reverse Hölder class RHq(ℝn) with q > n/2. In this paper, by the regularity estimate of the fractional heat kernel related with L, we establish the quantitative weighted boundedness of Littlewood ...
Li Yang, Pengtao Li, Andrea Scapellato
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Journal of Logic and Analysis, 2022 Lusin's Theorem states that, for every Borel-measurable function $\bf{f}$ on $\mathbb R$ and every $ε>0$, there exists a continuous function $\bf{g}$ on $\mathbb R$ which is equal to $\bf{f}$ except on a set of measure $<ε$. We give a proof of this result using computability theory, relating it to the near-uniformity of the Turing jump operator ...
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Two‐dimensional metric spheres from gluing hemispheres
Journal of the London Mathematical Society, Volume 106, Issue 4, Page 3069-3102, December 2022., 2022 Abstract We study metric spheres (Z,dZ)$(Z, d_{Z} )$ obtained by gluing two hemispheres of S2$\mathbb {S}^{2}$ along an orientation‐preserving homeomorphism g:S1→S1$g \colon \mathbb {S}^{1} \rightarrow \mathbb {S}^{1}$, where dZ$d_{Z}$ is the canonical distance that is locally isometric to S2$\mathbb {S}^{2}$ off the seam. We show that if (Z,dZ)$(Z, d_{
Toni Ikonen
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Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022 Let (X, d, μ) be a metric measure space endowed with a metric d and a non‐negative Borel doubling measure μ. Let L be a non‐negative self‐adjoint operator on L2(X). Assume that the (heat) kernel associated to the semigroup e−tL satisfies a Gaussian upper bound.
Jiawei Shen +3 more
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A Generalization of Lusin's Theorem [PDF]
Proceedings of the American Mathematical Society, 1975 In this note we characterize σ \sigma -
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Haar null and Haar meager sets: a survey and new results
Bulletin of the London Mathematical Society, Volume 52, Issue 4, Page 561-619, August 2020., 2020 Abstract We survey results about Haar null subsets of (not necessarily locally compact) Polish groups. The aim of this paper is to collect the fundamental properties of the various possible definitions of Haar null sets, and also to review the techniques that may enable the reader to prove results in this area.
Márton Elekes, Donát Nagy
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