A Quantitative Lusin Theorem for Functions in BV
نویسندگان
چکیده
We extend to the BV case a measure theoretic lemma previously proved by DiBenedetto, Gianazza and Vespri ([1]) in W 1,1 loc . It states that if the set where u is positive occupies a sizable portion of a open set E then the set where u is positive clusters about at least one point of E. In this note we follow the proof given in the Appendix of [3] so we are able to use only a 1−dimensional Poincaré inequality.
منابع مشابه
p-Lambda-bounded variation
A characteriation of continuity of the $p$-$Lambda$-variation function is given and the Helly's selection principle for $Lambda BV^{(p)}$ functions is established. A characterization of the inclusion of Waterman-Shiba classes into classes of functions with given integral modulus of continuity is given. A useful estimate on modulus of variation of functions of class $Lambda BV^{(p)}$ is found.
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