WebReal & Complex Analysis Qualifying Exam Solution, Spring 2010 Shiu-Tang Li January 1, 2013 A-1 (a) Given >0, P(jf n f mj> ) < 1 p R 1 0 jf n(x) f m(x)jpdx. Therefore, for each j2N, there exists N j such that P(jf n f mj> 1 2 j) < 1 2 for every n;m N j. If we choose n= N j;m= N j+1, and de ne A j:= fjf N j f N j+1 j> 1 2 j g, we nd that f N (x ... WebREAL ANALYSIS QUALIFYING EXAM SOLUTIONS September 20, 2007 A passing grade is 6 problems done completely correctly, or 5 done completely correctly with substantial …
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