0000000001024564

AUTHOR

Nijjwal Karak

0000-0002-7595-9748

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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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