Results 1 to 10 of about 215 (138)

On Banach and Kuratowski Theorem, K-Lusin sets and strong sequences

Open Mathematics, 2018
In 2003 Bartoszyński and Halbeisen published the results on various equivalences of Kuratowski and Banach theorem from 1929 concerning some aspect of measure theory.
Jureczko Joanna
doaj   +3 more sources

The Lusin Theorem and Horizontal Graphs in the Heisenberg Group

Analysis and Geometry in Metric Spaces, 2013
In this paper we prove that every collection of measurable functions fα , |α| = m, coincides a.e. withmth order derivatives of a function g ∈ Cm−1 whose derivatives of order m − 1 may have any modulus of continuity weaker than that of a Lipschitz ...
Hajłasz Piotr, Mirra Jacob
doaj   +5 more sources

A Quantitative Lusin Theorem for Functions in BV [PDF]

Springer INdAM Series, 2015
We extend to the BV case a measure theoretic lemma previously proved by DiBenedetto et al. (Atti Accad. Naz. Lincei Cl. Sci. Mat. Appl. 9, 223–225, 2006) in W loc 1, 1. It states that if the set where u is positive occupies a sizable portion of an open set E then the set where u is positive clusters about at least one point of E. In this note we follow
Vincenzo Vespri, Vespri Vincenzo
exaly   +5 more sources

On the double Lusin condition and convergence theorem for Kurzweil-Henstock type integrals [PDF]

Mathematica Bohemica, 2016
Equiintegrability in a compact interval $E$ may be defined as a uniform integrability property that involves both the integrand $f_n$ and the corresponding primitive $F_n$.
Abraham Racca, Emmanuel Cabral
doaj   +3 more sources

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
core   +2 more sources

A generalization of Lusin’s theorem [PDF]

Proceedings of the American Mathematical Society, 1975
In this note we characterize σ \sigma -finite Riesz measures that allow one to approximate measurable functions by continuous functions in the sense of Lusin’s theorem.
Michael L. Wage
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Lusin-type Theorems for Cheeger Derivatives on Metric Measure Spaces

Analysis and Geometry in Metric Spaces, 2015
A theorem of Lusin states that every Borel function onRis equal almost everywhere to the derivative of a continuous function. This result was later generalized to Rn in works of Alberti and Moonens-Pfeffer.
Guy C. David
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The Riemann-Cantor uniqueness theorem for unilateral trigonometric series via a special version of the Lusin-Privalov theorem [PDF]

Proceedings of the American Mathematical Society, 2017
Using Baire's theorem, we give a very simple proof of a special version of the Lusin-Privalov theorem and deduce via Abel's  theorem the  Riemann-Cantor theorem on the uniqueness of the coefficients of pointwise convergent unilateral trigonometric ...
Mortini, Raymond
core   +3 more sources

A Lusin type theorem for gradients

Journal of Functional Analysis, 1991
Let $\Omega$ be an open subset of $R^n$, $n>1$, with finite measure and let $f:\Omega\to R^n$ be a Borel vector field on $\Omega$. Then, for every $\epsilon>0$, there exists a function $u$ on $\Omega$ of class $C^1$ such that $f$ agrees with the ...
ALBERTI, GIOVANNI
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A Remark on the Theorems of Lusin and Egoroff

Canadian Mathematical Bulletin, 1964
In this note we do not intend to establish new results but only to suggest a very simple proof of Lusin's theorem, direct for σ-finite regular measures, a proof that bypasses the usual procedure of first ...
Elias Zakon
core   +2 more sources