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In: Advanced Math

Analysis Integral confused concept. Please clear writing and follow the comment 1. upper sum with respect...

Analysis Integral confused concept. Please clear writing and follow the comment

1. upper sum with respect to P is U(f,P)= sum of Mk(xk-xk-1). Does that equal to U(f)=inf{u(f,P): p is a element of Q} (Q is the collection of all possible partition})

Also, is Mk=sup{f(x):x is a element of {xk-1,xk}?????

2. If Q is a refinement of P, then U(f, Q)<=U(f, P) and L(f, P),<=L(f,Q). I don't understand the geometric meaning behind this because Q has more element than P and contains all of the elements from P, However, why U(f, Q)<=U(f, P)????

This Q is not the Q from question1

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Colby Messinger answered 1 year ago
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