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math104-s21:s:antonthan [2021/05/08 00:12] 45.48.153.5 [Problem 18] |
math104-s21:s:antonthan [2026/02/21 14:41] (current) |
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| $$U(f) \leq \sup_n(U(f, P_n)) = lim R_n = \inf_n(L(f, P_n)) \leq L(f)$$ | $$U(f) \leq \sup_n(U(f, P_n)) = lim R_n = \inf_n(L(f, P_n)) \leq L(f)$$ | ||
| - | Since we also have $L(f) = U(f)$ by integrability, | + | Since we also have $L(f) = U(f)$ by integrability, |
| === (b) === | === (b) === | ||
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| ===== ඞ ඞ ඞ ඞ ඞ ===== | ===== ඞ ඞ ඞ ඞ ඞ ===== | ||
| - | {{ :math104: | + | {{ math104-s21: |