Let f be a Lebesgue integrable function that's equal to 0 for all x not in [a,b] Let g be a function that is equal to 0 for all x not in a interval [-d,d] and suppose that g is C^ Is the function h(x) = f(x)*g(x) integrable?
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Originally Posted by southprkfan1 Let f be a Lebesgue integrable function that's equal to 0 for all x not in [a,b] Let g be a function that is equal to 0 for all x not in a interval [-d,d] and suppose that g is C^ Is the function h(x) = f(x)*g(x) integrable? Your function is bounded (continuous on a segment), hence is integrable.
Originally Posted by Laurent Your function is bounded (continuous on a segment), hence is integrable. I can "see" how that would follow, but I'm not entirely sure the formal proof. EDIT: Would it be that: where K is the upper bound of g?
Last edited by southprkfan1; March 27th 2010 at 02:24 PM.
Originally Posted by southprkfan1 I can "see" how that would follow, but I'm not entirely sure the formal proof. EDIT: Would it be that: where K is the upper bound of g? No, it would be
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