We extend to the BV case a measure theoretic lemma previously proved by DiBenedetto, Gianazza and Vespri in $W^{1,1}_{loc}$ . It states that if the set where u is positive occupies a sizable portion of an open set E then the set where u is positive clusters about at least one point of E.
A Quantitative Lusin Theorem for Functions in BV / Telcs, Andras; Vespri, Vincenzo. - STAMPA. - (2015), pp. 81-87. [10.1007/978-3-319-02666-4_4]
A Quantitative Lusin Theorem for Functions in BV
VESPRI, VINCENZO
2015
Abstract
We extend to the BV case a measure theoretic lemma previously proved by DiBenedetto, Gianazza and Vespri in $W^{1,1}_{loc}$ . It states that if the set where u is positive occupies a sizable portion of an open set E then the set where u is positive clusters about at least one point of E.
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