Results 111 to 120 of about 327,917 (135)

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 establishing this theorem for sets of finite measure only.
openaire   +1 more source

On Lusin’s Theorem for Non-additive Measure

Advances in Intelligent and Soft Computing, 2011
In this paper, we prove Lusin’s theorem remains valid for nonadditive Borel measure under the conditions of weakly null additivity, continuity from above and a certain additional continuity.
Tamaki Tanaka, Toshikazu Watanabe
exaly   +2 more sources

A SAITÔ–TOMITA–LUSIN THEOREM FOR JB*-TRIPLES AND APPLICATIONS

Quarterly Journal of Mathematics, 2006
Non-commutative versions of the classical theorems by Egoroff and Lusin were provided in [\textit{M.\,Tomita}, Math.\ J.\ Okayama Univ.\ 9, 63--98 (1959; Zbl 0204.14605)] and [\textit{K.\,Saito}, Tohoku Math.\ J. (2) 19, 332--340 (1967; Zbl 0161.11002)] in the context of \(C^*\)-algebras. In the paper under review, those results are extended to \(JB^*\)
Francisco José Fernandez Polo, Antonio M Peralta, Francisco J Fernández-Polo   +2 more
exaly   +3 more sources

A Lusin theorem for a class of Choquet capacities

Statistical Papers, 2002
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Castaldo, Adriana, Marinacci, Massimo
openaire   +1 more source

The Theorems of Lusin and Egoroff

1971
A real-valued function f on R is called measurable if f−1(U) is measurable for every open set U in R. f is said to have the property of Baire if f −1 (U) has the property of Baire for every open set U in R. In either definition, U may be restricted to some base, or allowed to run over all Borel sets.
openaire   +1 more source

Lusin's theorem for measure preserving homeomorphisms

Mathematika, 1979
We are concerned with invertible transformations of the unit n-dimensional cube In, 2 ≤ n ≤ ∞, which preserve n-dimensional Lebesgue measure μ. Following Halmos [4], we denote the space of all such transformations by G = G(In), and the subset of G consisting of homeomorphisms by M = M(In). We ask to what extent, and in what sense, can we approximate an
Alpern, Steve, Edwards, Robert D.
openaire   +2 more sources

A lusin-type theorem for vector fields on the wiener space

Doklady Mathematics, 2010
The paper extends \textit{G. Alberti's} [J. Funct. Anal. 100, No. 1, 110--118 (1991; Zbl 0752.46025)] result on Borel vector fields on infinite dimensional Gaussian spaces. The methodology involves estimates that do not depend on the dimension.
openaire   +2 more sources

A Lusin theorem for nonlocal gradients

We extend the celebrated result of Alberti, stating that Borel vector fields coincide with gradients of $C^1$-functions outside of a set of arbitrary small measure. We prove that a similar statement holds true in the setting of fractional gradients and $C^{0,s}-functions.
openaire   +1 more source

A Constructive Version of the Lusin Separation Theorem

2009
I state and prove a constructive version of the Lusin Separation Theorem. The classical statement of the theorem is that disjoint analytic sets are Borel separable. The definitions and results are carried out in the axiom system CZF for constructive set theory.
openaire   +1 more source

Lusin's First Separation Theorem

Journal of the London Mathematical Society, 1971
openaire   +1 more source