Search results for "Lebesgue's number lemma"

showing 4 items of 4 documents

Generalized Lebesgue points for Sobolev functions

2017

In this article, we show that a function $f\in M^{s,p}(X),$ $0<s\leq 1,$ $0<p<1,$ where $X$ is a doubling metric measure space, has generalized Lebesgue points outside a set of $\mathcal{H}^h$-Hausdorff measure zero for a suitable gauge function $h.$

Discrete mathematicsDominated convergence theoremmedian010102 general mathematicsLebesgue's number lemmaRiemann integralSobolev spaceLebesgue integration01 natural sciencesLebesgue–Stieltjes integrationFunctional Analysis (math.FA)Mathematics - Functional Analysis010101 applied mathematicssymbols.namesakemetric measure spaceDifferentiation of integralsSquare-integrable function46E35 28A78FOS: MathematicssymbolsLocally integrable function0101 mathematicsgeneralized Lebesgue pointMathematicsCzechoslovak Mathematical Journal
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On a normal form of symmetric maps of [0, 1]

1980

A class of continuous symmetric mappings of [0, 1] into itself is considered leaving invariant a measure absolutely continuous with respect to the Lebesgue measure.

Discrete mathematicsPure mathematicsLebesgue measureLebesgue's number lemmaStatistical and Nonlinear Physics58F20Absolute continuityLebesgue integrationLebesgue–Stieltjes integrationsymbols.namesakeNonlinear system28D05symbolsInvariant (mathematics)Borel measureMathematical PhysicsMathematicsCommunications in Mathematical Physics
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Generality of Henstock-Kurzweil type integral on a compact zero-dimensional metric space

2011

ABSTRACT A Henstock-Kurzweil type integral on a compact zero-dimensional metric space is investigated. It is compared with two Perron type integrals. It is also proved that it covers the Lebesgue integral.

General MathematicsInjective metric spaceMathematical analysisLebesgue's number lemmaHenstock-kurzweil integral Perron integral derivation basisRiemann–Stieltjes integralRiemann integralLebesgue integrationVolume integralsymbols.namesakeDifferentiation of integralsSettore MAT/05 - Analisi MatematicasymbolsDaniell integralMathematics
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Riesz and Wolff potentials and elliptic equations in variable exponent weak Lebesgue spaces

2015

Submitted by Alexandre Almeida (jaralmeida@ua.pt) on 2015-11-12T11:41:07Z No. of bitstreams: 1 RieszWolff_RIA.pdf: 159825 bytes, checksum: d99abdf3c874f47195619a31ff5c12c7 (MD5) Approved for entry into archive by Bella Nolasco(bellanolasco@ua.pt) on 2015-11-17T12:18:41Z (GMT) No. of bitstreams: 1 RieszWolff_RIA.pdf: 159825 bytes, checksum: d99abdf3c874f47195619a31ff5c12c7 (MD5) Made available in DSpace on 2015-11-17T12:18:41Z (GMT). No. of bitstreams: 1 RieszWolff_RIA.pdf: 159825 bytes, checksum: d99abdf3c874f47195619a31ff5c12c7 (MD5) Previous issue date: 2015-04

Pure mathematicsWolff potentialScale (ratio)Weak Lebesgue spaceVariable exponentMathematics::Classical Analysis and ODEsLebesgue's number lemmaNon-standard growth conditionIntegrability of solutionssymbols.namesakeMathematics - Analysis of PDEsReal interpolationFOS: MathematicsLp spaceMathematicsLaplace's equationMathematics::Functional AnalysisVariable exponentIntegrability estimatesRiesz potentialApplied MathematicsMathematical analysisFunctional Analysis (math.FA)Mathematics - Functional AnalysissymbolsRiesz potential47H99 (Primary) 46B70 46E30 35J60 31C45 (Secondary)Analysis of PDEs (math.AP)
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