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Math Help - Polynomial integrable on bounded sets

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    Polynomial integrable on bounded sets

    Hello,

    i have a few questions about a proof. Let P be a polynomial of degree m :
    P:\mathbb{R}^n ->\mathbb{R} , P(x_1 ,...,x_n)=a_m \prod\limits_{j=1}^{m-1}\ (x_1 - q_j (x_2 ,..., x_n))


    Now we want to show that (\left|P(x)\right|)^{-\sigma} with \sigma <1/m is integrable on bounded sets.
    The author argues as follows: For any A < \infty, there is a B < \infty , s.t. for \sigma <1/m we get:
    \int\limits_{-A}^A (\left|P(x)\right|)^{-\sigma} dx_1 \leq B for \left|(x_2 ,.., x_n)\right| \leq A
    So first of all i think, because P is a polynomial it has only finite many zeros. Therefore we can think about the integration area without these singularities. But why does the inequality hold?


    edit: excuse me, there was something wrong. Now the proposition is correct. I forgot a minus in the exponent, that is  - \sigma instead of \sigma.

    Please help me with my problem
    Regards
    Last edited by Sogan; July 22nd 2011 at 12:23 PM.
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