R. Latala, K. Oleszkiewicz: On the best constant in the Khintchine-Kahane inequality, Studia Math. 109(1), 101-104, 1994. 41 Home/Search Document Not in Database Summary Related Articles |
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A few notes on Statistical Learning Theory - Mendelson (2003) (2 citations) (Correct)
....that # F 1 n. Proof: By the assumption on # F , there is some f F for which # = E f 1 n. Applying the Kahane Khintchine s inequality, there is an absolute constant c such that for every x 1 , x n 2 (in fact c = 1 # 2 will su#ce, as shown in [14]) Hence, R n (F ) cE . Define g(X 1 , X n ) n 1 (X i ) and since f is bounded by 1 then Eg f . By Bernstein s inequality (theorem 2.20) and selecting x = nmE g for some integer m, c n 2 m 2 (E g) 2 f n nmE g . 39 But since E g = # then the ....
R. Latala, K. Oleszkiewicz: On the best constant in the Khintchine-Kahane inequality, Studia Math. 109(1), 101-104, 1994. 41
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