I canīt read your post.
i want to show, that
Here P is a polynomial of order m in and M,q are some constants.
We know that for some constant q.
But why is the first integral finite?
I hope, you can see it now.
I have a idea, how to solve this problem. But i'm not sure, whether this way is correct.
We know that
Can i conclude, that the set has finite measure? Why is this correct?
Take a close look at P(x). and q. Consider what you have and when it would be a problem.
If q >= 0, P(x) ^ q is just a polynomial (possibyl degenerate). That should be finite.
If q < 0, there would be a problem only if P(a) = 0 for some 'a' in [-1,1].
However, if it's going to be a problem for some 'a' in [-1,1], we have that last piece of information.
Did we get anywhere?