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- 18:58, 14 July 2008 (diff | hist) . . (0) . . 8.5 Old Kiwi
- 18:58, 14 July 2008 (diff | hist) . . (0) . . 8.5 OldKiwi
- 18:57, 14 July 2008 (diff | hist) . . (+1,112) . . 8.5 Old Kiwi
- 18:57, 14 July 2008 (diff | hist) . . (+1,112) . . 8.5 OldKiwi
- 18:28, 14 July 2008 (diff | hist) . . (+236) . . N 8.5 Old Kiwi (New page: 8a) Given such an <math>r<s</math> for any <math>p \in (r,s)</math> we have <math>\int_X |f|^p = \int_{\{x:|f|\leq 1 \}} |f|^p+\int_{\{x:|f|> 1 \}} |f|^p \leq \int_{\{x:|f|\leq 1 \}} |f|...)
- 18:28, 14 July 2008 (diff | hist) . . (+236) . . N 8.5 OldKiwi (New page: 8a) Given such an <math>r<s</math> for any <math>p \in (r,s)</math> we have <math>\int_X |f|^p = \int_{\{x:|f|\leq 1 \}} |f|^p+\int_{\{x:|f|> 1 \}} |f|^p \leq \int_{\{x:|f|\leq 1 \}} |f|...)
- 18:21, 14 July 2008 (diff | hist) . . (+30) . . Problem Set 8 Old Kiwi
- 18:21, 14 July 2008 (diff | hist) . . (+29) . . Problem Set 8 OldKiwi
- 14:59, 13 July 2008 (diff | hist) . . (+230) . . Problem Set 7 7.6 OldKiwi (current)
- 14:59, 13 July 2008 (diff | hist) . . (+230) . . Problem Set 7 7.6 Old Kiwi (current)
- 15:56, 10 July 2008 (diff | hist) . . (+2) . . Problem Set 7 7.6 Old Kiwi
- 15:56, 10 July 2008 (diff | hist) . . (+2) . . Problem Set 7 7.6 OldKiwi
- 15:56, 10 July 2008 (diff | hist) . . (+972) . . N Problem Set 7 7.6 Old Kiwi (New page: 6. First we show <math>f_n\rightarrow f </math> in <math> L^p</math>. Let <math>\delta > 0</math>. Let <math> \epsilon = \frac {\delta }{1+2^{p+1}} </math> Then by Egorov <math>\exists ...)
- 15:56, 10 July 2008 (diff | hist) . . (+972) . . N Problem Set 7 7.6 OldKiwi (New page: 6. First we show <math>f_n\rightarrow f </math> in <math> L^p</math>. Let <math>\delta > 0</math>. Let <math> \epsilon = \frac {\delta }{1+2^{p+1}} </math> Then by Egorov <math>\exists ...)
- 15:22, 10 July 2008 (diff | hist) . . (+44) . . Team 2: The Sharks awesome answers Old Kiwi
- 15:22, 10 July 2008 (diff | hist) . . (+43) . . Team 2: The Sharks awesome answers OldKiwi
- 15:37, 8 July 2008 (diff | hist) . . (+1,808) . . N Exam 3.5 Old Kiwi (New page: 5) Fix <math>\alpha > 0</math>. Define <math>f_{n_k}</math> inductively as follows. Let <math>f_{n_{0}}=f_1</math> Let <math>\epsilon_1 = 1</math> Let <math>A_1=[0,\alpha+1]</math>. ...) (current)
- 15:37, 8 July 2008 (diff | hist) . . (+1,808) . . N Exam 3.5 OldKiwi (New page: 5) Fix <math>\alpha > 0</math>. Define <math>f_{n_k}</math> inductively as follows. Let <math>f_{n_{0}}=f_1</math> Let <math>\epsilon_1 = 1</math> Let <math>A_1=[0,\alpha+1]</math>. ...) (current)
- 14:41, 8 July 2008 (diff | hist) . . (+35) . . Practice Exam 3 Old Kiwi
- 14:41, 8 July 2008 (diff | hist) . . (+34) . . Practice Exam 3 OldKiwi
- 14:39, 8 July 2008 (diff | hist) . . (+762) . . N Exam 3.4 Old Kiwi (New page: 4a) <math>0 \leq sin^n(x)\leq 1</math> on <math>[0, \pi]</math> and 1 is integrable on <math>[0,\pi]</math>, so by Leb. Dom. Conv. Thm.: <math> lim_n \int_0^{\pi}sin^n(x)dx= \int_0^{\pi...) (current)
- 14:39, 8 July 2008 (diff | hist) . . (+762) . . N Exam 3.4 OldKiwi (New page: 4a) <math>0 \leq sin^n(x)\leq 1</math> on <math>[0, \pi]</math> and 1 is integrable on <math>[0,\pi]</math>, so by Leb. Dom. Conv. Thm.: <math> lim_n \int_0^{\pi}sin^n(x)dx= \int_0^{\pi...) (current)
- 14:22, 8 July 2008 (diff | hist) . . (-1) . . Practice Exam 3 Old Kiwi
- 14:22, 8 July 2008 (diff | hist) . . (-1) . . Practice Exam 3 OldKiwi
- 14:22, 8 July 2008 (diff | hist) . . (+36) . . Practice Exam 3 Old Kiwi
- 14:22, 8 July 2008 (diff | hist) . . (+35) . . Practice Exam 3 OldKiwi
- 14:04, 8 July 2008 (diff | hist) . . (+583) . . Exam 3.3 Old Kiwi (current)
- 14:04, 8 July 2008 (diff | hist) . . (+583) . . Exam 3.3 OldKiwi (current)
- 13:49, 8 July 2008 (diff | hist) . . (+1,136) . . N Exam 3.3 Old Kiwi (New page: 3a) Suppose that there is such an <math>f</math>. Then we may choose <math>N</math> large enough such that <math>m(\{x:f^*<f\}\cap[-N,N])>0</math>. Call this set <math>A</math>. Let <m...)
- 13:49, 8 July 2008 (diff | hist) . . (+1,136) . . N Exam 3.3 OldKiwi (New page: 3a) Suppose that there is such an <math>f</math>. Then we may choose <math>N</math> large enough such that <math>m(\{x:f^*<f\}\cap[-N,N])>0</math>. Call this set <math>A</math>. Let <m...)
- 13:12, 8 July 2008 (diff | hist) . . (+35) . . Practice Exam 3 Old Kiwi
- 13:12, 8 July 2008 (diff | hist) . . (+34) . . Practice Exam 3 OldKiwi
- 13:10, 8 July 2008 (diff | hist) . . (+55) . . Exam3.2 Old Kiwi (current)
- 13:10, 8 July 2008 (diff | hist) . . (+55) . . Exam3.2 OldKiwi (current)
- 13:07, 8 July 2008 (diff | hist) . . (+348) . . Exam3.2 Old Kiwi
- 13:07, 8 July 2008 (diff | hist) . . (+348) . . Exam3.2 OldKiwi
- 12:59, 8 July 2008 (diff | hist) . . (+459) . . Exam3.2 Old Kiwi
- 12:59, 8 July 2008 (diff | hist) . . (+459) . . Exam3.2 OldKiwi
- 12:46, 8 July 2008 (diff | hist) . . (+920) . . Exam3.2 Old Kiwi
- 12:46, 8 July 2008 (diff | hist) . . (+920) . . Exam3.2 OldKiwi
- 12:15, 8 July 2008 (diff | hist) . . (+342) . . N Exam3.2 Old Kiwi (New page: 2a. <math>( \Rightarrow )</math> Say <math>f</math> is A.C. Then <math>f</math> is of bounded variation, and since <math>f</math> is clearly nondecreasing, <math>f</math> must be bounded...)
- 12:15, 8 July 2008 (diff | hist) . . (+342) . . N Exam3.2 OldKiwi (New page: 2a. <math>( \Rightarrow )</math> Say <math>f</math> is A.C. Then <math>f</math> is of bounded variation, and since <math>f</math> is clearly nondecreasing, <math>f</math> must be bounded...)
- 12:08, 8 July 2008 (diff | hist) . . (-6) . . Practice Exam 3 Old Kiwi
- 12:08, 8 July 2008 (diff | hist) . . (-6) . . Practice Exam 3 OldKiwi
- 12:07, 8 July 2008 (diff | hist) . . (+2) . . Practice Exam 3 Old Kiwi
- 12:07, 8 July 2008 (diff | hist) . . (+2) . . Practice Exam 3 OldKiwi
- 12:07, 8 July 2008 (diff | hist) . . (+38) . . Practice Exam 3 Old Kiwi
- 12:07, 8 July 2008 (diff | hist) . . (+37) . . Practice Exam 3 OldKiwi
- 12:19, 5 July 2008 (diff | hist) . . (+336) . . N Solution to number 3 Old Kiwi (New page: 3) Define <math>f(x)=\sum_{n=1}^\infty n\chi_{[2^{-n}, 2^{-(n-1)})}(x)</math> Then <math>\forall p \in (0, \infty), \ \int_0^1 |f|^p=\sum_{n=1}^\infty \frac{n^p}{2^n}<\infty</math> by t...) (current)
- 12:19, 5 July 2008 (diff | hist) . . (+336) . . N Solution to number 3 OldKiwi (New page: 3) Define <math>f(x)=\sum_{n=1}^\infty n\chi_{[2^{-n}, 2^{-(n-1)})}(x)</math> Then <math>\forall p \in (0, \infty), \ \int_0^1 |f|^p=\sum_{n=1}^\infty \frac{n^p}{2^n}<\infty</math> by t...) (current)
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