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Math Help - Dirichlet function upper and lower sum

  1. #1
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    Dirichlet function upper and lower sum

    Question:

    Suppose that f(x)=7 if x is rational and f(x)=3 if x is irrational on the interval [1,3]. Let P be a partition of [1,3].

    What is the lower sum: I have that the lower sum is 0.

    What is the upper sum: I have that the upper sum is 4.

    What is sup L(f,P) over all partitions: 7

    What is inf U(f,P) over all partitions: 3

    And that the function is integrable over [1,3]

    Am I on the right track with this?
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: Dirichlet function upper and lower sum

    Quote Originally Posted by CountingPenguins View Post
    And that the function is integrable over [1,3]
    Lebesgue-integrable, but not Riemann-integrable.
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  3. #3
    MHF Contributor Also sprach Zarathustra's Avatar
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    Re: Dirichlet function upper and lower sum

    Quote Originally Posted by CountingPenguins View Post
    Question:

    Suppose that f(x)=7 if x is rational and f(x)=3 if x is irrational on the interval [1,3]. Let P be a partition of [1,3].

    What is the lower sum: I have that the lower sum is 0.

    What is the upper sum: I have that the upper sum is 4.

    What is sup L(f,P) over all partitions: 7

    What is inf U(f,P) over all partitions: 3

    And that the function is integrable over [1,3]

    Am I on the right track with this?

    Look here:


    http://www.mathhelpforum.com/math-he...tml#post664645
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