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Properties of integration on Jordan Regions and stuff

  1. Mar 11, 2008 #1
    1. The problem statement, all variables and given/known data


    Let f : Rn ----> R.
    i) Let E1 and E2 be two Jordan regions in Rn such that E1 C E2 Suppose f is integrable
    on E2. Then, show that f is integrable on E1.
    ii) Suppose f is continuous on Rn. Then, show that f is integrable on any Jordan region
    E in Rn. Here, E is bounded.


    3. The attempt at a solution

    These both seem really easy to me and i cant figure it out.


    For part two, is it enough to show that E is of measure zero? and how do you do that?
     
  2. jcsd
  3. Mar 11, 2008 #2

    HallsofIvy

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    Staff Emeritus
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    How do you define integrable? Suppose f were NOT integrable on E1. What would that tell you about the integral on E2?

    As for (ii), you are told only that E is bounded. Why in the world would you think that it has measure 0?
     
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