Results 1 to 10 of about 57 (57)

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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Effectivizing Lusin’s Theorem

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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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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On the Property N-1

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, Małgorzata Turowska   +1 more
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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.
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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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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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On a Theorem of Banach and Kuratowski and $K$-Lusin Sets

Rocky Mountain Journal of Mathematics, 2003
In a paper of 1929, Banach and Kuratowski proved, assuming the continuum hypothesis, a combinatorial theorem which implies that there is no non-vanishing sigma-additive finite measure on the real line which is defined for every set of reals. It will be shown that the combinatorial theorem is equivalent to the existence of a K-Lusin set of size the ...
Halbeisen, Lorenz, Bartoszynski, T.
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