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RESEARCH PRODUCT

Generalized Lebesgue points for Sobolev functions

Nijjwal Karak

subject

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 pointMathematics

description

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 $h.$

https://doi.org/10.21136/cmj.2017.0405-15