Search results for "Dominated convergence theorem"

showing 2 items of 2 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 the integration of Riemann-measurable vector-valued functions

2016

We confine our attention to convergence theorems and descriptive relationships within some subclasses of Riemann-measurable vector-valued functions that are based on the various generalizations of the Riemann definition of an integral.

Dominated convergence theoremRiemann-measurable functionPure mathematicsMeasurable functionGeneral Mathematics02 engineering and technologyLebesgue measurable gaugeLebesgue integration01 natural sciencessymbols.namesakeConvergence (routing)0202 electrical engineering electronic engineering information engineeringCalculusMathematics (all)0101 mathematicsMathematicsBirkhoff McShane Henstock and Pettis integralMathematics::Complex Variables010102 general mathematicsRiemann integralRiemann hypothesisBounded variationBounded variationAlmost uniform convergencesymbols020201 artificial intelligence & image processingVector-valued function$$ACG_*$$ACG∗and $$ACG_delta ^*$$ACGδ∗functionMonatshefte für Mathematik
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