The question is: Let . Prove that if is a closed Jordan domain, and is Riemann integrable, then . (How to relate the condition it's Riemann integrable to the value is ? The textbook I use define is integrable on iff )
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Originally Posted by ianchenmu The question is: Let . Prove that if is a closed Jordan domain, and is Riemann integrable, then . (How to relate the condition it's Riemann integrable to the value is ? The textbook I use define is integrable on iff ) What is the (L) and (U)? In any case, since the integral exists, it must be zero since the set you're integrating over has Lebesgue measure zero.
Originally Posted by Gusbob What is the (L) and (U)? In any case, since the integral exists, it must be zero since the set you're integrating over has Lebesgue measure zero. , , where , where . ( is an Jordan region in , is a bounded function, is an n-dimensional rectangle s.t. . is a grid on . (Extend to by setting for .)) Can you use these backgrounds and terminologies to explain? Thanks!
Last edited by ianchenmu; Mar 31st 2013 at 02:35 AM.
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