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December 5th, 2015, 09:59 PM  #1 
Newbie Joined: Dec 2015 From: East US Posts: 1 Thanks: 0  Question about Multiple Integration
Can someone here solve this? I am desperate, I made an account just for this. I have solved parts one and two of this problem, but c and d are driving me insane: c) f,g are real valued functions on a subset, A, of R^n. Show that if the integral of f and g over A exist, then the integral of fg over A exists. d) Again, f has the same conditions as before, but let B be a subset of A. Show that if the integral of f exists and B has volume, then the integral of f over B exists. Help on either would be incredible! Volume refers to Jordan measure and integration is Riemann type. Last edited by skipjack; December 6th, 2015 at 12:25 AM. 
December 6th, 2015, 05:16 PM  #2 
Senior Member Joined: Aug 2012 Posts: 2,357 Thanks: 740 
Off the top of my head for (c) you can squeeze any Riemann sum for fg between one for min(f)min(g) and max(f)max(g). For (d) I'd look at the function g = f on B and 0 on A\B. You still have to do all the details but that's how I'd get started. 

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integration, multiple, question, real analysis, riemann 
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