Results 11 to 20 of about 337,654 (135)
On Dahlberg’s Lusin area integral theorem [PDF]
Proceedings of the American Mathematical Society, 1995 We give new proofs to the Lusin area integral theorem of Dahlberg. Our techniques rely on the theory of elliptic boundary value problems on nonsmooth domains and are shown to extend to other important cases, including systems of equations.
Marius Mitrea
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The Lusin-Privalov theorem for subharmonic functions [PDF]
Proceedings of the American Mathematical Society, 1996 This paper establishes a generalization of the Lusin-Privalov radial uniqueness theorem which applies to subharmonic functions in all dimensions. In particular, it answers a question of Rippon by showing that no subharmonic function on the upper half-space can have normal limit
Mortini, Raymond
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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 -
Michael L. Wage
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A refined Lusin type theorem for gradients
Journal of Functional AnalysisWe prove a refined version of the celebrated Lusin type theorem for gradients by Alberti, stating that any Borel vector field $f$ coincides with the gradient of a $C^1$ function $g$, outside a set $E$ of arbitrarily small Lebesgue measure. We replace the Lebesgue measure with any Radon measure $μ$, and we obtain that the estimate on the $L^p$ norm of ...
De Masi, Luigi, Marchese, Andrea
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A Saito-Tomita-Lusin theorem for JB*-triples and applications
, 2006 A theorem of Lusin is proved in the non-ordered context of JB*-triples. This is applied to obtain versions of a general transitivity theorem and to deduce refinements of facial structure in closed unit ballls of JB*-triples and ...
Bunce, L. J. +3 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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Lusin-type theorem for functions with prescribed gradient [PDF]
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 ...
PRATI, EMANUELE
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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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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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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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