1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Lebesgue integral(jordan measurable)

  1. Nov 30, 2011 #1
    Hi!

    I have a guess. Could you give me your opinion about my guess??

    Let A be a rectifiable set(or jordan measurable set).This is defined in a book "Analysis on manifolds" by munkres. You can refer to it in p.112-113.
    Now, let f be a bounded function over the set A, and suppose f is integrable over A.
    Then [itex]\int[/itex][itex]_{A}[/itex]f = [itex]\int[/itex][itex]_{I}[/itex]g where I is a large rectangle containg the set A and g is a function with domain I whose a value at x[itex]\in[/itex]A is f(x) and a value at x[itex]\in[/itex]I-A is 0.
    Then under this assumption, A is measurable, f is also measurable on A, and f is lebesgue integrable over A and the lebesgue integral and [itex]\int[/itex][itex]_{A}[/itex]f are equal.

    Is my guess true??
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?