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Math Help - Jordan Content Question

  1. #1
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    Jordan Content Question

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  2. #2
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    Suppose there exists y\in V such that f(y)>0 then since f is continous and V open there exists an r>0 such that for all x\in B_r(y) \subset V we have f(x)>0 and since B_r(y) is Jordan measurable \int_{B_r(y)} f >0 a contradiction.
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  3. #3
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    Quote Originally Posted by Jose27 View Post
    Suppose there exists y\in V such that f(y)>0 then since f is continous and V open there exists an r>0 such that for all x\in B_r(y) \subset V we have f(x)>0 and since B_r(y) is Jordan measurable \int_{B_r(y)} f >0 a contradiction.
    But what if f(y) can be both positive or negative?
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  4. #4
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    If it's negative use the exact same argument with the inequalities reversed, and note that continuity is crucial since it lets us pick a ball around y where f is positive (or negative).
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