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Real Analysis Conception Question 1. Lemma: if P is a subset of Q, then L(f,p)<=L(f,Q) and U(f,P)>=U(f,Q) why???...

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Real Analysis Conception Question

1. Lemma: if P is a subset of Q, then L(f,p)<=L(f,Q) andU(f,P)>=U(f,Q)

why??? for P is a subset of Q, however, why the upper sum ofU(f,P) is even bigger than or equal to U(f,Q) it doesn't make anysense. Please

draw the geometric description to help with clear handwritten

2. Let's assume the partition={x0,x1...xn} of the interval[a,b]

what is the diference between m=inf{f(x):x is a element of[a,b]} and mk=inf{f(x):x is a element of [xk-1,xk]}

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