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Unformatted text preview: ( m , n ) . Show that there exists a realvalued Function f in L 2 () For which k f n f k 2 0 as n , by the Following steps. (i) Show that sup n N k f n k 2 < . (ii) Show that there is no loss oF generality in supposing f n 0 For all n . Hint: Consider f n . (iii) Show that { f 2 n : n N } is a Cauchy sequence in L 1 () . (iv) Show that there exists a Function g in L 1 () with g 0 and  f 2 n g  0. (v) Show that g L 2 () and k f n g k 2 0. Hint:  f n g  f n + g . (vi) Anything more to do?...
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This note was uploaded on 11/21/2009 for the course STAT 330 taught by Professor Davidpollard during the Spring '09 term at Yale.
 Spring '09
 DavidPollard
 Statistics, Probability

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