1.Let P_1 and P_2 be partitions of ﹝a,b﹞.Show that if P_1 is a refinement
of P_2 then || P_1 || < = || P_2 ||
2.A function f:﹝a,b﹞→ R is Lipschitz if there is some K >= 0 such that
for any x,y in ﹝a,b﹞, |f(x)-f(y)| < = K|x-y|.
Q: If P is a partition of ﹝a,b﹞, show that
0 < = U(f,p)-L(f,P) < = K(b-a)|| P ||.
3.Let the function f:﹝a,b﹞→ R be monotonically decreasing and let P_n be
the nth regular partition.
Q: Show that U(f,p)-L(f,P)= 1/n ﹝f(a)-f(b)﹞﹝b-a﹞
希望各位給一些提示或幫我解答 謝謝
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